FormulAI

Trigonometry

Trigonometric ratios, identities, and laws.

Pythagorean Identity
sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1
Law of Sines
asin⁡A=bsin⁡B=csin⁡C=2R\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R
Law of Cosines
c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab \cos C
Sine of a Sum
sin⁡(α+β)=sin⁡αcos⁡β+cos⁡αsin⁡β\sin(\alpha + \beta) = \sin\alpha \cos\beta + \cos\alpha \sin\beta
Cosine of a Sum
cos⁡(α+β)=cos⁡αcos⁡β−sin⁡αsin⁡β\cos(\alpha + \beta) = \cos\alpha \cos\beta - \sin\alpha \sin\beta
Sine Double Angle
sin⁡(2x)=2sin⁡xcos⁡x\sin(2x) = 2\sin x\cos x
Cosine Double Angle
cos⁡(2x)=cos⁡2x−sin⁡2x\cos(2x) = \cos^2 x - \sin^2 x
Tangent Definition
tan⁡x=sin⁡xcos⁡x\tan x = \frac{\sin x}{\cos x}
Cotangent Definition
cot⁡x=cos⁡xsin⁡x=1tan⁡x\cot x = \frac{\cos x}{\sin x} = \frac{1}{\tan x}

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