Question

For the interval $[-2\pi ,2\pi ],\cos x>0$ in the interval

• A. $(-2\pi ,-\pi )\cup (\pi ,2\pi )$
• B. $(-2\pi ,-\frac{3\pi }{2})\cup (-\frac{\pi }{2},\frac{\pi }{2})\cup (\frac{3\pi }{2},2\pi )$
• C. $[-2\pi ,-\frac{\pi }{2}]\cup [\frac{\pi }{2},2\pi ]$
• D. $[-\frac{\pi }{2},\frac{\pi }{2}]$

Answer 1

The correct option is B $(-2\pi ,-\frac{3\pi }{2})\cup (-\frac{\pi }{2},\frac{\pi }{2})\cup (\frac{3\pi }{2},2\pi )$

From the graph of $\cos x$,
we see that $\cos x>0$ for the interval $(-2\pi ,-\frac{3\pi }{2})\cup (-\frac{\pi }{2},\frac{\pi }{2})\cup (\frac{3\pi }{2},2\pi )$