question_answer

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

Correct Answer: A

Solution :

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 \[1\].