Question

For the interval $[-2\pi ,2\pi ],\sin x<0$ in the interval

• A. $(-\pi ,0)\cup (\pi ,2\pi )$
• B. $(-2\pi ,2\pi )-\left\{0\right\}$
• C. $(-2\pi ,-\pi )\cup (0,\pi )$
• D. $[-\frac{\pi }{2},\frac{\pi }{2}]$

Answer 1

The correct option is A $(-\pi ,0)\cup (\pi ,2\pi )$

From the graph of $\sin x$,

we see that $\sin x<0\forall (-\pi ,0)\cup (\pi ,2\pi )$