Formulas & tables/Mathematics/Trigonometry

Trigonometry

9 formulas · Mathematics

Trigonometric functions in a right triangle
sin⁡α=ac, cos⁡α=bc, tan⁡α=ab\sin\alpha=\tfrac{a}{c},\ \cos\alpha=\tfrac{b}{c},\ \tan\alpha=\tfrac{a}{b}
Pythagorean trigonometric identity
sin⁡2α+cos⁡2α=1\sin^2\alpha+\cos^2\alpha=1
Tangent as a ratio
tan⁡α=sin⁡αcos⁡α\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}
Sine of a double angle
sin⁡2α=2sin⁡αcos⁡α\sin 2\alpha=2\sin\alpha\cos\alpha
Cosine of a double angle
cos⁡2α=cos⁡2α−sin⁡2α\cos 2\alpha=\cos^2\alpha-\sin^2\alpha
Sine of a sum or difference of angles
sin⁡(α±β)=sin⁡αcos⁡β±cos⁡αsin⁡β\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta
Cosine of a sum or difference of angles
cos⁡(α±β)=cos⁡αcos⁡β∓sin⁡αsin⁡β\cos(\alpha\pm\beta)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta
Radian measure
180∘=π rad180^\circ=\pi\ \text{rad}
Sum and difference of sines
sin⁡α+sin⁡β=2sin⁡α+β2cos⁡α−β2\sin\alpha+\sin\beta=2\sin\tfrac{\alpha+\beta}{2}\cos\tfrac{\alpha-\beta}{2}