1. (2007 Sichuan High School Mathematics Competition Preliminary Test Question) Among the following functions, which one is both an increasing function in $\left[0, \frac{\pi}{2}\right]$ and has $\pi$ as its smallest positive period?
A. $y=|\sin x|$
B. $y=\mathrm{e}^{\sin \frac{1}{2} x}$
C. $y=\sin 2 x$
D. $y=\cos 4 x$
1. A When $x \in\left[0, \frac{\pi}{2}\right]$, $y=|\sin x|=\sin x$, which is monotonically increasing. Also, the smallest positive period of $y=|\sin x|$ is $\pi$, so the answer is A.