Arccosine
= Arccosine
{title2=$\arccos x$}
= Inverse cosine
{synonym}
For real $-1\leq x\leq1$, the principal arccosine is the unique angle $\theta\in[0,\pi]$ satisfying $\cos\theta=x$. Restricting to this interval makes the cosine one-to-one. Differentiating the identity on $-1<x<1$ gives $d(\arccos x)/dx=-1/\sqrt{1-x^2}$. Other solutions of $\cos\theta=x$ are $\theta=\pm\arccos x+2\pi n$, with integer $n$; an initial condition can select one of these branches.