Question

find all solutions in the interval (0, 2pi), rounded to five decimal places:

5cos2(theta) = 2

Answer 1

\(\bf 5cos^2(\theta)=2\implies cos^2(\theta)=\cfrac{2}{5}\implies cos(\theta)=\sqrt{\cfrac{2}{5}}\\ \quad \\
cos^{-1}[cos(\theta)]=cos^{-1}\left(\sqrt{\cfrac{2}{5}}\right)\implies \theta=cos^{-1}\left(\sqrt{\cfrac{2}{5}}\right)\)