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 $ .