1. (2007 National High School Mathematics League Jiangsu Region Preliminary Test) Given the function $y=\sin ^{2} x$, then the function
A. has the smallest positive period $2 \pi$
B. has the smallest positive period $\pi$
C. has the smallest positive period $\frac{\pi}{2}$
D. has no smallest positive period
1. B $y=\sin ^{2} x=\frac{1}{2}(1-\cos 2 x)$, then the smallest positive period $T=\pi$. Therefore, the answer is $\mathrm{B}$.