Parametric formulae

The parametric formulae express the sine, cosine and tangent of an angle $\alpha$ in terms of a single auxiliary variable, $t=\tan(\alpha/2)$. Their power is that they transform a linear equation in $\sin$ and $\cos$ into an ordinary rational equation in $t$: algebra takes the place of trigonometry. One must remember, however, that the passage to $t$ “loses” a particular case, which must always be checked separately.

• The parametric formulae
• Linear equations in sine and cosine