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© Matthew Pinkney 2003

Trigonometry Identities

This important identity can be derived as a direct result of Pythagoras's theorem, when applied to angles in trigonometry:

  • sin²x + cos²x = 1         (*)

Example

Suppose you know that sin30 = ½ . Then we can use the first formula above to work out cos30.

cos230 = 1 – sin230
so cos230 = 1 – ¼ = ¾
Hence cos30 = Ö3/2

 

Another useful identity is:

  • tan x = sin x / cos x

Example

tan 45 = sin45 / cos45
= (2/2)/(2/2)
= 1