The Cosine Function and Inverse Cosine Function

Cosine has domain $\mathbb{R}$ and range $[-1,1]$; its inverse is written $y=\cos^{-1}x$ or $y=\arccos(x)$. Since $\cos(x+2\pi)=\cos x$ for all $x$, but no smaller positive $p$ works for all $x$, cosine's period is $2\pi$ — the same period as sine, but the shape and the r …