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Series: Trigonometry: Other Advanced Identities


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About this Series

  • Lessons: 3
  • Total Time: 0h 25m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 08/13/2009
  • Last Updated At: 07/20/2010

In this three-lesson series, 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, power-reducing identities and half-angle 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. We'll first look at why these are true graphically and then we'll look at deriving them trigonometrically.

Power-reducing 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).

Half-angle 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 = +/- ((1-cos x)/2))^(1/2) and tan x/2 = +/- (1-cos 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 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

None of the lesson in this series have been reviewed.

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