Trigonometric Identities

Reciprocal Identities

• \csc \theta = \frac{1}{\sin \theta}

• \sin \theta = \frac{1}{\csc \theta}

• \sec \theta = \frac{1}{\cos \theta}

• \cos \theta = \frac{1}{\sec \theta}

• \cot \theta = \frac{1}{\tan \theta}

• \tan \theta = \frac{1}{\cot \theta}

• \tan \theta = \frac{\sin \theta}{\cos \theta}

• \cot \theta = \frac{\cos \theta}{\sin \theta}

Sum and Difference Identities

• \sin(a + b) = \sin(a)\cos(b) + \cos(a)\sin(b)

• \cos(a + b) = \cos(a)\cos(b) - \sin(a)\sin(b)

Pythagorean Identities

• \sin^2 \theta + \cos^2 \theta = 1

• 1 + \tan^2 \theta = \sec^2 \theta

• 1 + \cot^2 \theta = \csc^2 \theta

Double Angle Identities

• \sin(2a) = 2\sin(a)\cos(a)

• \cos(2a) = \cos^2(a) - \sin^2(a)

• \cos(2a) = 2\cos^2(a) - 1

• \cos(2a) = 1 - 2\sin^2(a)