Trigonometric Identities

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:

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

Reciprocal Identities:

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

Pythagorean Identities:

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

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