## Precalculus (6th Edition) Blitzer

Suppose $\theta =\cos^{-1} (3 \pi)$ This gives: $\cos \theta=\cos[\cos^{-1} (3 \pi)]$ The inverse property states that $\cos(\cos^{-1} a)=a$ satisfies for every $a$ in the range $[0,\pi]$ . But the value $a=3 \pi$ does not lie in the range of $[-1,1]$. Therefore, we have $\cos[\cos^{-1} (3 \pi)]$= Not defined