Question

The solution set of $\cos 5\theta =-\frac{1}{2}$ is

• A. $\theta =\frac{2n\pi }{5}\pm \frac{2\pi }{15},n\in Z$
• B. $\theta =\frac{2n\pi }{5}\pm \frac{2\pi }{3},n\in Z$
• C. $\theta =\frac{n\pi }{5}+(-1{)}^n(-\frac{\pi }{15}),n\in Z$
• D. $\theta =2n\pi \pm \frac{2\pi }{3},n\in Z$

Answer 1

The correct option is A $\theta =\frac{2n\pi }{5}\pm \frac{2\pi }{15},n\in Z$

$\cos 5\theta =-\frac{1}{2}\Rightarrow \cos 5\theta =\cos (\pi -\frac{\pi }{3})\Rightarrow \cos 5\theta =\cos \left(\frac{2\pi }{3}\right)\Rightarrow 5\theta =2n\pi \pm \frac{2\pi }{3}\Rightarrow \theta =\frac{2n\pi }{5}\pm \frac{2\pi }{15},n\in Z$