Trigonometry
Intermediate

Cosine of a Sum

Angle addition formula for cosine.

Formula

cos⁡(A+B)=cos⁡Acos⁡B−sin⁡Asin⁡B\cos(A+B) = \cos A\cos B - \sin A\sin B

Variables

A,BAngles

Example

cos 75° = cos(45°+30°) = cos45cos30 − sin45sin30 ≈ 0.259.

Did You Know?

These sum formulas let you compute the sine or cosine of an angle by breaking it into known pieces.

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