A inversa, a derivada, e a integral da função corda.

${\large cord\ \alpha = \sqrt{2(1 - \cos \alpha)}}$

Inversa: seja $arccord: \underset{x\ \mapsto\ arccord\ x}{[0, 2] \rightarrow [0, \pi]},\ \fbox{$arccord\ x = \arccos \left(1 - \dfrac{x^2}{2}\right)$}$.

Derivada: $\fbox{$(cord\ \alpha)' = \dfrac{\sin \alpha}{\sqrt{2 - 2\cos \alpha}}$}$.

Observemos que, para $0 \le \alpha \le 2\pi$, $cord\ \alpha = 2\sin \dfrac{\alpha}{2}$.

Logo,

$\fbox{$\displaystyle\int cord\ \alpha\ d\alpha\ =\ -4\cos \dfrac{\beta}{2} + c,\ \alpha = 2k\pi + \beta,\ k \in \mathbb{Z}, 0 \le \beta < 2\pi$}$.