Trigonometric Identities

Trigonometric Identities

Reciprocal Identities

• \frac{1}{\sin{x}} = \csc{x} , which also implies \frac{1}{\csc{x}} = \sin{x}

• \csc{x} = \frac{1}{\sin{x}}

• \sin{x} = \frac{1}{\csc{x}}

• \sec{x} = \frac{1}{\cos{x}}

• \cos{x} = \frac{1}{\sec{x}}

• \cot{x} = \frac{1}{\tan{x}}

• \tan{x} = \frac{1}{\cot{x}}

Quotient Identities

• \tan{x} = \frac{\sin{x}}{\cos{x}}

• \cot{x} = \frac{\cos{x}}{\sin{x}}

Pythagorean Identities

• \sin^2{\theta} + \cos^2{\theta} = 1

• 1 + \tan^2{\theta} = \sec^2{\theta}

• 1 + \cot^2{\theta} = \csc^2{\theta}

Other Identities

• 1 - \cos^2{x} = \sin^2{x}

• 1 + \tan^2{x} = \sec^2{x}

• \frac{1}{\cos^2{x}} = \sec^2{x}

• \frac{\cos{x}}{\sin{x}} = \cot{x}

• \frac{1}{\sin{x}} = \csc{x}

• \frac{1}{\cos^2 x} = \sec^2 x