# Trigonometric Identity

## Trigonometric Identity

Name given to certain relationships that exist between various trigonometric ratios.

### Symbol

We sometimes use the symbol “≡” for trigonometric identities.

Some of these identities are fundamental and result from the study of the right triangle :

sin (A) = $$\dfrac{a}{c}$$,   csc (A) = $$\dfrac{c}{a}$$,   cos (A) = $$\dfrac{b}{c}$$,   sec (A) = $$\dfrac{c}{b}$$,   tan (A) = $$\dfrac{a}{b}$$,   cot (A) = $$\dfrac{b}{a}$$

Other identities result from the study of the trigonometric circle :

• $$\sin^2 (θ) + \cos^2 (θ) = 1$$
• $$1 + \tan^2 (θ) = \sec^2 (θ)$$
• $$\cot^2 (θ) + 1 = \textrm{csc}^2 (θ)$$