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