Trigonometric Functions — Formula Sheet

l = r\theta

\theta_{\text{rad}} = \theta_{\text{deg}} \times \frac{\pi}{180}

\theta_{\text{deg}} = \theta_{\text{rad}} \times \frac{180}{\pi}

\sin \theta = y

\cos \theta = x

\tan \theta = \frac{y}{x}

\cot \theta = \frac{x}{y}

\sec \theta = \frac{1}{x}

\sin^2\theta + \cos^2\theta = 1

1 + \tan^2\theta = \sec^2\theta

1 + \cot^2\theta = \cosec^2\theta

\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B

\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B

\tan(A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}

On the unit circle, for any angle θ, sinθ = y-coordinate, cosθ = x-coordinate.

tanθ = sinθ/cosθ, defined when cosθ ≠ 0.