Chapter 4.2, Problem 51E

To determine

To (a) show that q is a critical point if $\cos 4\theta =-\cos 2\theta$ (b) show,using a unit circle, that $\cos {\theta }_1=-\cos {\theta }_2$ if and only if ${\theta }_1=\pi \pm {\theta }_2+2\pi k$ for an integer k, (c) show that $\cos 4\theta =-\cos 2\theta$ if and only if $\theta =\frac{\pi }{2}+2\pi k\text{ or }\theta =\frac{\pi }{6}+\left(\frac{\pi }{3}\right)k$ (d) find the critical points and (e) the check the results against a graph of the function.