high School⏱ 4 min

Sum/Difference Formulas

sin(a+b) and cos(a+b)

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α=30°β=45°α+β=75°
α = 30°
β = 45°
sin⁡(30°+45°)=sin⁡30°cos⁡45°+cos⁡30°sin⁡45°=0.9659\sin(30°+45°)=\sin30°\cos45°+\cos30°\sin45°=0.9659
cos⁡(30°+45°)=cos⁡30°cos⁡45°−sin⁡30°sin⁡45°=0.2588\cos(30°+45°)=\cos30°\cos45°-\sin30°\sin45°=0.2588

Sum formulas are derived from rotation in the complex plane. Green vector = rotating blue by angle β = the sum angle.