Trigonometry
Intermediate

Sine of a Sum

Angle addition formula for sine.

Formula

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

Variables

A,BAngles

Example

sin 75° = sin(45°+30°) = sin45cos30 + cos45sin30 ≈ 0.966.

Did You Know?

The angle-sum formulas are the mathematical heart of how audio signals combine and interfere.

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