Trigonometric Identities

This is a list of the basic trigonometric identities. You may want to work through a tutorial, with examples and detailed solutions, on Using Trigonometric Identities.



Review

Pythagoren Identities


  1. sin2x + cos2x = 1

  2. tan2x + 1 = sec2x

  3. 1 + cot2x = csc2x

Reciprocal Identities


  1. csc x = 1 / sin x

  2. sec x = 1 / cos x

  3. cot x = 1 / tan x

The Tangent and Cotangent Identities


  1. tan x = sin x / cos x

  2. cot x = cos x / sin x

Identities for Negatives


  1. sin (-x) = - sin x (the sine function is an odd function)

  2. cos (-x) = cos x (the cosine function is an even function)

  3. tan (-x) = - tan x (the tangent function is an odd function)


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Updated: 2 April 2013

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