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Period of Trigonometric Function

Source: 2017 AMC 12B #7

February 16, 2017
AMCAMC 12AMC 12 Bfunction2017 AMC 12B

Problem Statement

The functions sin⁡(x)\sin(x) and cos⁡(x)\cos(x) are periodic with least period 2π2\pi. What is the least period of the function cos⁡(sin⁡(x))\cos(\sin(x))?
<spanclass=′latex−bold′>(A)</span> π2<spanclass=′latex−bold′>(B)</span> π<spanclass=′latex−bold′>(C)</span> 2π<spanclass=′latex−bold′>(D)</span> 4π<spanclass=′latex−bold′>(E)</span><span class='latex-bold'>(A)</span>\ \frac{\pi}{2}\qquad<span class='latex-bold'>(B)</span>\ \pi\qquad<span class='latex-bold'>(C)</span>\ 2\pi\qquad<span class='latex-bold'>(D)</span>\ 4\pi\qquad<span class='latex-bold'>(E)</span> It's not periodic.
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