Addition, double-angle and half-angle formulae

The functions $\sin$ and $\cos$ are not linear: in general $\sin(\alpha+\beta)\ne\sin\alpha+\sin\beta$. There exists, however, a collection of formulae that allow the sine, cosine and tangent of the sum of two angles to be expressed in terms of the sines and cosines of the individual summands. These formulae are the foundation of the whole of algebraic trigonometry and come into play in all the subsequent chapters: trigonometric equations, trigonometry of triangles, complex numbers and analytic geometry in space. From them one then derives the double-angle formulae (by setting $\beta=\alpha$) and the half-angle formulae (which express the sine and cosine of $\alpha/2$ starting from $\cos\alpha$).

Sections

• Addition and subtraction formulae
• Double-angle formulae
• Half-angle formulae

Exercises

• All the worked exercises of the chapter