# Trigonometric Identities

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

## List of identities

Given two functions f and g, we say f = g if f(x) = g(x) for all every x in the domain of both f and g.

Quotient identities:

${\displaystyle \tan(\theta )={\frac {\sin(\theta )}{\cos(\theta )}}~\cot(\theta )={\frac {\cos(\theta )}{\sin(\theta )}}}$

Reciprocal Identities:

${\displaystyle \csc(\theta )={\frac {1}{\sin(\theta )}}~\sec(\theta )={\frac {1}{\cos(\theta )}}~\cot(\theta )={\frac {1}{\tan(\theta )}}}$

Pythagorean Identities:

${\displaystyle \sin ^{2}(\theta )+\cos ^{2}(\theta )=1~\tan ^{2}(\theta )+1=\sec ^{2}(\theta )~\cot ^{2}(\theta )+1=\csc ^{2}(\theta )}$

Even-Odd:

Sine, Cosecant, Tangent, and Cotangent are all odd functions, so f(-x) = -f(x). The other two trigonometric functions cos and secant are even, so f(-x) = f(x)

 Return to Topics Page