Question

The number of roots of the equation sin x = 1, lying between $-4\pi$ and $4\pi$, is

• A. 8
• B. 6
• C. 4
• D. 0

Answer 1

The correct option is C 4

Interval, $[-4\pi ,4\pi ]$ is equivalent to $[0,8\pi ]$
Now, in interval, $[0,2\pi ]$ as one full quadrant.
$\sin x=1$
$\sin x=\sin \frac{\pi }{2}$
There is only one value in one full quadrant. There are 4 such full quadrants in $[0,8\pi ]$
Hence, there are 4 such values.