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Trigonometric Identities & Formulas

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Pythagorean Identity

$\sin^2(θ) + \cos^2(θ) = 1$

Sum of Angles for Sine

$\sin(α + β) = \sin(α)\cos(β) + \cos(α)\sin(β)$

Sum of Angles for Cosine

$\cos(α + β) = \cos(α)\cos(β) - \sin(α)\sin(β)$

Double Angle Formula for Sine

$\sin(2θ) = 2\sin(θ)\cos(θ)$

Double Angle Formula for Cosine

$\cos(2θ) = \cos^2(θ) - \sin^2(θ)$

Tangent of Sum

$\tan(α + β) = \frac{\tan(α) + \tan(β)}{1 - \tan(α)\tan(β)}$

Law of Sines

$\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}$

Law of Cosines

$c^2 = a^2 + b^2 - 2ab\cos(C)$

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