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Series: Trigonometry: Trigonometric Functions

About this Series

  • Lessons: 28
  • Total Time: 3h 51m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 08/13/2009
  • Last Updated At: 06/01/2011

In these 28 lessons Trigonometry lessons, we'll learn the basics of trigonometric functions. We'll start out with a look at angles, radian measure, and arc lengths. We'll learn about different types of angles (coterminal angles, supplementary angles, complementary angles, acute angles, right angles, straight angles, obtuse angles, etc) and cover an approach to use to determine if two angles are coterminal and another technique that will help you determine which quadrant an angle lies in. After a thorough coverage of the basics of angles, we'll move on to learn about radians, which most mathematicians prefer when finding angle measure, and the arc length formula.

Next, we'll focus on right angle trig. The trigonometric functions of an angle are defined to be the ratios of the side lengths of a right triangle having that as an angle. The three basic trig functions are sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent). Their reciprocals are the cosecant, secant, and cotangent functions, respectively. In addition to defining each of the trig functions, we'll also look at some basic examples to see how they work when we're dealing with triangles with actual angle and side measures. Additionally, we'll learn how to use these functions and the Pythagorean theorem to find the value of missing angles and side lengths in right triangles.

Our third chunk of lessons will introduce us to basic math that involves trigonometric fuctions. We'll start by learning how to evaluate trig functions for an angle in the coordinate plane. Then, we'll learn how to evaluate trig functions using reference angles. Next, we'll cover how to find the value of various trig functions given information about other trig functions. Last, we'll cover trig functions for important angles (that are commonly used).

Then, we'll turn our attention to graphing trig functions. We'll start with sine and cosine functions. Then, we'll learn about how the graphs change when a coefficient is added (e.g. to make 4 sin x or to make sin 4x), how to find the maxima, minima and zeros for the sine and cosine functions, how the graphs of these functions shift when a constant is added to them, and how phase shifts impact these graphs. We'll also look at a common application of sine and cosine curves: wave motion, such as that of sound waves or water.

Once you've mastered the basics of graphing sine and cosine functions, it's time to move on to the other trig functions: tangent, cotangent, cosecant, and secant. We'll walk through the same graphing lessons for these functions as we did for sine and cosine.

Last, we'll turn our focus to inverse trig functions and an example trig word problem. We'll introduce and define inverse trig functions and their domain and range restrictions. Once we understand what inverse trigonometric functions are, we'll learn how to evaluate them when we're faced with them. Once we know what inverse trig functions are and how to evaluate them in isolation, we'll want to learn how to solve equations that involve them. Then, we'll learn to evaluate the composition of a trig function and its inverse and why certain answers (that we'll lay out) are not allowed when solving an inverse trig function.

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 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

2174 lessons

Founded in 1997, Thinkwell has succeeded in creating "next-generation" 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 technology-based textbooks. For more information about Thinkwell, please visit or visit Thinkwell's Video Lesson Store at

Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

Lessons Included

bait and switch
~ mslingerland

We bought onto your site to try to find out how to find any theta when given a trig function and you showed us 30,60, 90 and 45, 45, 90 - which is pretty basic.
very disappointed

Does not use sin or cos
~ eshoemaker

Faulty advertising! I don't like thinking I am getting an example of something that I want to understand and have the problem be something simple like d=rt.

Pre-Calculus: Graphing Period, Amplitude, Shifts
~ sotake

Extremely helpful--the textbook I'm using leaves some points unexplained, but Professor Burger explains everything clearly and concisely.

~ Elena8

Clear and Simple

Good trick!
~ Terri7

To help memorize the trig values of 30, 45, 60 & 90 degrees, without having to go back to the special triangles.

good and straight forward
~ Michael131

This lesson is quick but very good.

So helpful!
~ greenshoes

Prof Burger is a mastermind! Everything from the set up of the problem to the end and everything in between is so helpful! Prof Burger has given me so much confidence with math I plan to take my schools entire calc series!

it's ok
~ Brayan

He only concentrated on the trigonometric funtions but did not show how to really use the protactor.

Below are the descriptions for each of the lessons included in the series:

Supplementary Files: