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PreCalculus: Fundamental Trigonometric Identities 
Trigonometry: Finding All Function Values 
PreCalculus: Simplifying Using Trig Identities 
Trigonometry: Simplify Fractional Trig Expression 
Trigonometry: Simplify Trig Function Binomial Prod 
PreCalculus: Factoring Trigonometric Expressions 
PreCalculus: Trig Functions  Odd, Even, Neither? 
Trigonometry: Proving an Identity 
Trigonometry: Proving an Identity: Other Examples 
PreCalculus: Solving Trigonometric Equations 
PreCalculus: Solving Trig Equations by Factoring 
PreCalculus: Trig Equations with Coefficients 
PreCalculus: Trig Equations and Quadratic Formula 
PreCalculus: Word Problems and Trig Equations 
Trigonometry: Angle Sum & Difference Identities 
PreCalculus: Using Sum and Difference Identities 
Trigonometry: Sum & Difference Identities 
Trigonometry: Confirming a DoubleAngle Identity 
PreCalculus: Using DoubleAngle Identities 
Trigonometry: MultipleAngle Identities Word Probs 
Trigonometry: Using a Cofunction Identity 
Trigonometry: Using a PowerReducing Identity 
Trigonometry: HalfAngle Identities,Trig Equations
About this Series
 Lessons: 23
 Total Time: 3h 5m
 Use: Watch Online & Download
 Access Period: Unlimited
 Created At: 08/13/2009
 Last Updated At: 06/01/2011
In this 23lesson series, we'll look at an assortment of trigonometric identities that will be tremendously helpful in evaluating trig expressions, solving trig equations, and simplifying trigonometric expressions. We'll start with the derivation and explanation of the four fundamental trig identities (tan x = sin x / cos x; cos^2 x + sin^2 x = 1; 1 + tan^2 x = sec^2 x; and 1+ cot^2 x = csc^2 x), and we'll learn how we can use these identities to find the values of the other trigonometric functions given the value of a trigonometric function for an angle and the quadrant that the angle lies in. We'll then generate proofs based upon these identities to establish extension identities that also hold.
We'll then look at several techniques for simplifying trig expressions  factoring, multiplying binomial products, restating expressions in terms of only sines and cosines, etc. We can apply several of these same techniques and others to equations to solve trig identities, which we'll also practice.
We'll next turn to sum and difference identities. These trigonometric identities will help you find trig values for the sums and differences of angles. The sine of the sum of two angles, x and y, is equal to sin (x + y) = sin x cos y + cos x sin y. We'll go through this identity as well as identities for differences of angles and cosine and tangent.
We'll also cover the doubleangle identities. Doubleangle identities can help you solve trigonometric equations like our example: cos 2x = sin x (where x is between 0 and 2*pi). They are also commonly needed to simplify trig expressions or solve word problems like the one we'll go through.
Last, we'll look at a few additional advanced trigonometric identities that can be used to help you solve trig equations or simplify trig expressions: cofunction identities, powerreducing identities and halfangle identities. The cofunction identities relate sine to cosine and tangent to cotangent: cos (x pi/2) = sin x and sin (x  pi/2) = cos x and tan (x  pi/2) = cot x. Powerreducing identities allow you to write trig expressions with powers as equivalent expressions without powers: cos^2 x = (1 + cos (2x) ) / 2 and sin ^2 x = (1  cos (2x)) / 2. These formulas are useful in solving trig equations and simplifying trig expressions that contain powers of trig functions (including powers in excess of 2). Halfangle identities allow you to write trig functions of an angle x/2 (half of the angle x) in terms of trig functions of the angle x: cos x/2 = +/ ((1+cos x)/2))^(1/2) and sin x/2 = +/ ((1cos x)/2))^(1/2) and tan x/2 = +/ (1cos x)/sin x
Taught by Professor Edward Burger, this bundle of lessons was selected from a broader, comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers an algebra review, trigonometric functions, trigonometric identities, applications of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
About this Author
 Thinkwell
 2174 lessons
 Joined:
11/13/2008
Founded in 1997, Thinkwell has succeeded in creating "nextgeneration" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technologybased textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.
Thinkwell lessons feature a starstudded cast of outstanding university professors: Edward Burger (PreAlgebra through...
Lessons Included
 PreCalculus: Fundamental Trigonometric Identities
 Trigonometry: Finding All Function Values
 PreCalculus: Simplifying Using Trig Identities
 Trigonometry: Simplify Fractional Trig Expression
 Trigonometry: Simplify Trig Function Binomial Prod
 PreCalculus: Factoring Trigonometric Expressions
 PreCalculus: Trig Functions  Odd, Even, Neither?
 Trigonometry: Proving an Identity
 Trigonometry: Proving an Identity: Other Examples
 PreCalculus: Solving Trigonometric Equations
 PreCalculus: Solving Trig Equations by Factoring
 PreCalculus: Trig Equations with Coefficients
 PreCalculus: Trig Equations and Quadratic Formula
 PreCalculus: Word Problems and Trig Equations
 Trigonometry: Angle Sum & Difference Identities
 PreCalculus: Using Sum and Difference Identities
 Trigonometry: Sum & Difference Identities
 Trigonometry: Confirming a DoubleAngle Identity
 PreCalculus: Using DoubleAngle Identities
 Trigonometry: MultipleAngle Identities Word Probs
 Trigonometry: Using a Cofunction Identity
 Trigonometry: Using a PowerReducing Identity
 Trigonometry: HalfAngle Identities,Trig Equations
Below are the descriptions for each of the lessons included in the series:

PreCalculus: Fundamental Trigonometric Identities
In this lesson, Professor Burger will reveal and explain several basic trigonometric identity proofs. He will begin by reviewing the definitions of sine, cosine, and tangent. From these definititions, he will prove tanx = sinx/cosx. Then, he uses the Pythagorean Theorem to show you the proofs for 3 more trigonometric identities: cos^2 + sin^2 = 1, 1+ tan^2 = sec^2, and 1 + cot^2 = csc^2. Finally, Professor Burger will tell you which of these identities and proofs you need to memorize and which you can derive simply and don't need to fret about memorizing in advance of your test.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: Finding All Function Values
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

PreCalculus: Simplifying Using Trig Identities
Professor Burger demonstrates how to use the fundamental trigonometric identities to simplify complex triognometric expressions. Many seemingly complex expressions can be greatly simplified with simple application of several trigonometric identities. You will practice using expressions such as tanx * cosx and [1+(tan^2)x]/(csc^2)x. In these problems, you will see how substituting 1/cos^2 for sec^2 or 1/sin for csc or sin/cos for tan. By applying the definitions of the different trig functions, you'll often be able to substantially simplify a problem to the point where it will be very easy for you to evaluate and solve it.
This lesson is perfect for review for a CLEP test, midterm, final, summer school, or personal growth!
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: Simplify Fractional Trig Expression
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: Simplify Trig Function Binomial Prod
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

PreCalculus: Factoring Trigonometric Expressions
Just as you can simplify trigonometric expressions using the trig identities, you can often simplify the expressions by factoring, as you would with other types of expressions. Simplifying using the identities and factoring will save you a lot of effort in solving trig problems. In order to recognize opportunities to factor when working trigonometric problems, Professor Burger recommends that you use trigonometry identities to convert trig functions to sin and cos, whenever possible. Some examples you will learn how to simplify include (sin^2) x+ (sin^2)x(cos^2)x and sinx  (cos^2)x  1 and sin^2x + (2/cscx)+x.
This lesson is perfect for review for a CLEP test, midterm, final, summer school, or personal growth!
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

PreCalculus: Trig Functions  Odd, Even, Neither?
In this lesson, Professor Burger teaches you how to determine if a function is even, odd, or neither. He begins by defining even and odd functions and graphing them. A function is even if the function of negative x is equal to the function of x. The graph of an even function is symetric across the yaxis. A function is odd if the function of negative x is equal to the negative function of x. The graph of an odd function is symetric around the origin. After defining these, Professor Burger identifies whether sin and cos are even or odd, and then shows several more examples, including tan x, sin (2x), (sin x)/x, and x cos x. Lastly, Professor Burger describes and illustrates what a function looks like that is neither odd nor even. In this case, it is not symmetric to the Y axis or the origin.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: Proving an Identity
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: Proving an Identity: Other Examples
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

PreCalculus: Solving Trigonometric Equations
This lesson will teach you how to solve equations involving trigonometric functions. Professor Burger shows you two ways to look at these equations, on a graph, and using reference angles. You will learn to rephrase the equation to determine what it is really asking, ""What value of X makes the function of X = n?"" You will learn how to write your answer to indicate infinitely many solutions and the stepbystep process of solving the equations. Examples of problems covered in this lesson involve trig functions, roots, fractions, variables and coefficients, including problems like cos x = 1/2 and sinx = (2^(1/2)/2). You'll also learn when and why most trig problems like these have multiple (or infinite) solutions and how to correctly identify and denote these solution sets.
This lesson is perfect for review for a CLEP test, midterm, final, summer school, or personal growth!
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

PreCalculus: Solving Trig Equations by Factoring
Professor Burger teaches how to solve more complicated equations (tanx * sin^2x = tan x) involving trigonometric functions in this lesson. Solving these types of problems involve use of trig identities, factoring, etc and how to find all of the viable solutions for these types of problems. In the problem listed above, Professor Burger will show you how to factor the equation in order to help simplify and then solve it. Professor Burger also gives a warning about cancelling out in equations that involve trig functions. By canceling, you risk missing valid solutions and solution sets.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
About Professor Edward Burger:
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

PreCalculus: Trig Equations with Coefficients
Now that you have learned how to solve simple trigonometric equations, Professor Burger will show you how to solve trig equations that have a coefficient in the argument (e.g. sine of 2X versus just sine of X). These are also called multiple angle equations. In evaluating these trigonometry equations, you will generally only be asked to find solutions in one or two periods of the functions, so you will not have an infinite number of solutions (most often, you'll solve for solutions between 0 and 2*pi). Sample problems from this lesson include (2*sin 3*theta) = 1 and tan^2(2X) = 1 and sin2x*tan2x + sin2x = 0.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

PreCalculus: Trig Equations and Quadratic Formula
Sometimes, trigonometric equations cannot be factored. To solve these equations, Professor Burger shows you how to apply the quadratic formula to find solutions to these equations. This is a multistep process that starts with simplifying the equation. After the equation is simplified, you will be able to solve the quadratic formula and then enter that answer in to solve for X. In the lesson example, Professor Burger uses both a calculator and graphing to ensure he has the correct points. This lesson explains the covered material by walking through sample equations 3sin^2(2x) + sin (2x)1 = 0. This equation has 2 solutions over the interval from zero to 2*pi. This lesson is loaded with warnings about easy mistakes to make and pitfalls to be wary of when evaluating problems like this.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

PreCalculus: Word Problems and Trig Equations
This lesson provides a more realworld application of trigonometric equations using a word problem. Professor Burger walks you through solving the trig word problem about spring motion. The motion of the particular spring in question is described by the function: sin (2T)+ 3^(1/2)*cost (2T), where T is the time in seconds. The problem asks us to solve for all times, T, when the object is located where it started the experiment. As he demonstrates how to solve the word problem, Prof Burger uses many of the trig information he taught in previous lessons, including identities, graphing, and angles. Finally, he reminds you to check your answer to make sure that the solutions are allowable. Additionally, he highlights that you should 'reality check' your answer as it's obviously not possible to have solutions for T that are negative given that this is a realworld example and time should never be negative.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: Angle Sum & Difference Identities
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

PreCalculus: Using Sum and Difference Identities
Using the sum and difference identities, Professor Burger shows you how to solve a trig function for an unknown angle. For an example, he uses the sin(15 degrees). You can use known angle values for 45 degree and 30 degrees and the formula for the difference of two sines to find the solution. The formula for the difference of two sines is sin(x1  x2) = sinx1cosx2  cosx1sinx2. Hence, if you know what the sin and cos values of 30 and 45 degrees are, you should be able to plub them into this formula to arrive at the sine value of 15 degrees. The beauty of the sum and difference formulas for trig functions is that they allow us to decompose a problem we don't know the answer to into component parts to which we do know the answer, thus solving the original problem.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: Sum & Difference Identities
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: Confirming a DoubleAngle Identity
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

PreCalculus: Using DoubleAngle Identities
Doubleangle identities allow you to simplify trigonometric equations with a 2 as the coefficient. (similar formulae exist for trig functions with 1/2 or 3 as the coefficient). In this lesson, Professor Burger uses the equation cos2x = sinx as an example. If this equation were simply cos x = sinx, we could divide to rewrite the formula as sinx/cosx = tan x = 0, but in this case, we have a coefficient in advance of one of the arguments, which is why we need to use the doubleangle formulas. After using the doubleangle formulas in the provided example to simplify, you can further simplify these equations using trig identities (like the Pythagorean identity) and factoring. These tools will help you to solve many trig equations. The duble angle identities for sine, cosine, tangent and cotangent are: sin2x = 2sinxcosx, cos2x = cos^2xsin^2x, tan 2x = 2tanx/(1tan^2x), and cot2x = (cot^2x1)/2cotx.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: MultipleAngle Identities Word Probs
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: Using a Cofunction Identity
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: Using a PowerReducing Identity
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Trigonometry: HalfAngle Identities,Trig Equations
Taught by Professor Edward Burger, this lesson comes from a comprehensive course, Trigonometry. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/trigonometry. The full course covers trigonometric functions, trigonometric identities, application of trig, complex numbers, polar coordinates, exponential functions, logarithmic functions, conic sections, and more.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
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Still too abstract to get students (not math lovers;) exited....
awesome
When would you have a real problem where you would be looking for a position of a spring? I know that is what my students are going to be asking.
Great online video tutorial on how to verify if a trig function like sin or cos is even or odd. This question comes up on many college prep assessment tests and it's great to have these videos available for easy review online.
This lesson walks you through several different proofs of trig identities  he does a good job at going step by step and so I didn't get lost anywhere along the way. Great lesson!
Still a little confused but not because of tutorial.
This video was incredible! I was studying for ACTs when this question came up about odd functions...which I don't think I've ever encountered yet. But this is straightforward and worthwhile to watch. Thanks for making this tutorial  simply can't thank you enough!!! I'll definitely be looking out for some more tutorials :D