Parametric, sum-to-product and Werner formulae

With the addition formulae we know how to compute $\sin(\alpha+\beta)$ and $\cos(\alpha+\beta)$ from the individual summands. This chapter introduces two new “families of formulae” that come in useful in specific situations. The parametric formulae express $\sin$, $\cos$ and $\tan$ of $\alpha$ in terms of the single quantity $t=\tan(\alpha/2)$: they are the key to reducing linear trigonometric equations to rational equations. The Werner and sum-to-product formulae transform products into sums and sums into products: indispensable when a trigonometric expression needs to be factorised.

Sections

• Parametric formulae
• Sum-to-product and Werner formulae

Exercises

• All the worked exercises of the chapter