3. (2004 Tianjin City College Entrance Examination for Science) The smallest positive period of the function $y=\sin ^{1} x+\cos ^{2} x$ is
A. $\frac{\pi}{4}$
B. $\frac{\pi}{2}$
C. $\pi$
D. $2 \pi$
3. D $f(x+T)=f(x)$, that is, $\sin ^{2}(x+T)+\cos ^{2}(x+T)=\sin ^{4} x+\cos ^{2} x$. Taking $x=0$, we get $\sin ^{1} T+\cos ^{2} T$ $=1$. Upon inspection, when $T=\frac{\pi}{4}$ or $\frac{\pi}{2}$ or $\pi$, the above equation does not hold, so options $\mathrm{A}$, $\mathrm{B}$, and $\mathrm{C}$ are eliminated. Therefore, the answer is $\mathrm{D}$.