Question

The following equation involves multiple angles. Solve the equation on the interval [0, 2π). cos 4x= 1/2

Answer 1

`\cos(4x)=\cfrac{1}{2}\implies 4x=\cos^(-1)\left( \cfrac{1}{2} \right)\implies 4x= \begin{cases} (\pi )/(3)\\\\ (5\pi )/(3) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 4x=\cfrac{\pi }{3}\implies \boxed{x=\cfrac{\pi }{12}}~\hfill 4x=\cfrac{5\pi }{3}\implies \boxed{x=\cfrac{5\pi }{12}}`