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Basic Trigonometry Identities

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Pythagorean identity

$\sin^2(x) + \cos^2(x) = 1$

Quotient identity for tangent

$\tan(x) = \frac{\sin(x)}{\cos(x)}$

Quotient identity for cotangent

$\cot(x) = \frac{\cos(x)}{\sin(x)}$

Reciprocal identity for secant

$\sec(x) = \frac{1}{\cos(x)}$

Reciprocal identity for cosecant

$\csc(x) = \frac{1}{\sin(x)}$

Pythagorean identity for tangent and secant

$\tan^2(x) + 1 = \sec^2(x)$

Pythagorean identity for cotangent and cosecant

$\cot^2(x) + 1 = \csc^2(x)$

Co-function identity for sine and cosine

$\sin(x) = \cos(\frac{\pi}{2} - x)$

Co-function identity for tangent and cotangent

$\tan(x) = \cot(\frac{\pi}{2} - x)$

Even-odd identity for sine

$\sin(-x) = -\sin(x)$

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