Mathway | Trigonometry Formulas

Unit Circle

Unit Circle Values

Reciprocal Identities

$\sin θ = \frac{1}{\csc θ} \cos θ = \frac{1}{\sec θ} \tan θ = \frac{1}{\cot θ} \cot θ = \frac{1}{\tan θ} \sec θ = \frac{1}{\cos θ} \csc θ = \frac{1}{\sin θ}$

Ratio Indentities

$\tan θ = \frac{\sin θ}{\cos θ} \cot θ = \frac{\cos θ}{\sin θ}$

Pythagorean Identities

$\sin^{2} θ + \cos^{2} θ = 1 1 + \tan^{2} θ = \sec^{2} θ 1 + \cot^{2} θ = \csc^{2} θ$

Sum and Difference Formulas

$\sin (A + B) = \sin A \cos B + \cos A \sin B \sin (A - B) = \sin A \cos B - \cos A \sin B \cos (A + B) = \cos A \cos B - \sin A \sin B \cos (A - B) = \cos A \cos B + \sin A \sin B \tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \tan (A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$

Double-Angle Formulas

$\sin 2 A = 2 \sin A \cos A \cos 2 A = \cos^{2} A - \sin^{2} A = 2 \cos^{2} A - 1 = 1 - 2 \sin^{2} A \tan 2 A = \frac{2 \tan A}{1 - \tan^{2} A}$