Question

For a given integer $k$ , in the interval $\left[2\pi k-\frac{\pi }{2},2\pi k+\frac{\pi }{2}\right]$ the graph of $\sin x$ is

• A. increasing from $-1$ to $1$
• B. decreasing from $-1$ to $0$
• C. decreasing from $0$ to $1$
• D. none of the above

Answer 1

Answer: (A)

Since, $2\pi k-\frac{\pi }{2}\le \sin x\le 2\pi k+\frac{\pi }{2}$
For $k=0$ $-\pi /2<\sin x<\pi /2$ which increases from $-1$ to $1$ .
Similarly, for other values of $k$ it is increases from $-1$ to $1$ .