Arccos — Essentials

ESSENTIALS · FREE

Definition

$y = \arccos x \iff \cos y = x$ , with $D = [-1, 1]$ and $R = [0, \pi]$ . Never returns a negative angle.

$\arccos(-x) = \pi - \arccos x$ - reflects to an obtuse angle. Not odd. Do not borrow arcsin's sign flip.

$x$	$0$	$\dfrac{1}{2}$	$\dfrac{\sqrt{2}}{2}$	$\dfrac{\sqrt{3}}{2}$	$1$
$\arccos x$	$\dfrac{\pi}{2}$	$\dfrac{\pi}{3}$	$\dfrac{\pi}{4}$	$\dfrac{\pi}{6}$	$0$

Negative inputs: reflect. $\arccos\left(-\dfrac{1}{2}\right) = \pi - \dfrac{\pi}{3} = \dfrac{2\pi}{3}$ .

$\arcsin x + \arccos x = \dfrac{\pi}{2}$ for every $x$ in $[-1, 1]$ .

Whatever sits inside must satisfy $-1 \le \text{inside} \le 1$ .