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Basic Trigonometric Identities

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Pythagorean Identity

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

Quotient Identity for Tangent

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

Quotient Identity for Cotangent

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

Reciprocal Identity for Sine

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

Reciprocal Identity for Cosine

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

Reciprocal Identity for Tangent

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Reciprocal Identity for Cosecant

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

Reciprocal Identity for Secant

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

Reciprocal Identity for Cotangent

$\tan(\theta) = \frac{1}{\cot(\theta)}$

Pythagorean Identity for Tangent and Secant

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

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