Angle Addition

sin(A + B) and cos(A + B)

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $\sin(A + B) = \sin A\cos B + \cos A\sin B$.
• $\cos(A + B) = \cos A\cos B - \sin A\sin B$.
• Double angles: $\sin 2x = 2\sin x\cos x$ and $\cos 2x = 1 - 2\sin^2 x$.

Steps

1. A tempting mistake
2. The addition formulas
3. Test the formula
4. sin 75°
5. cos 105°
6. Double angles
7. cos 2x from sin x
8. Two triangles combined