3. The smallest positive period of the function $f(x)=|\sin x+\cos x|$ is
A. $\frac{\pi}{4}$
B. $\frac{\pi}{2}$
C. $\pi$
D. $2 \pi$
3. C $f(x)=|\sin x+\cos x|=\left|\sqrt{2} \sin \left(x+\frac{\pi}{4}\right)\right|$. Since $y=\sqrt{2} \sin \left(x+\frac{\pi}{4}\right)$ has a minimum positive period of $2 \pi$, and the graph of $f(x)=\left|\sqrt{2} \sin \left(x+\frac{\pi}{4}\right)\right|$ is obtained by reflecting the part of the graph of $y=\sqrt{2} \cdot \sin \left(x+\frac{\pi}{4}\right)$ below the $x$-axis to above the $x$-axis, its minimum positive period is $\pi$, hence the answer is $\mathrm{C}$.