3. The graph of the function $f(x)=A \cos (\omega x+\phi)$ is symmetric with respect to the origin if and only if ( )(where $k \in \mathbf{Z}$ ).
A. $\phi=2 k \pi+\frac{\pi}{2}$
B. $\frac{\varphi}{\omega}=2 k \pi \pm \frac{\pi}{2}$
C. $\phi=k \pi+\frac{\pi}{2}$
D. $\phi=k \pi+\frac{\pi}{2}$ or $\omega x=k \pi$
3. C
$f(x)=\operatorname{Aoox}(\omega x$ ' $\varphi)$ 的图像关 $f \cdot$ 拍点对称 $\Leftrightarrow f(x)$ 图像过原点 $\Leftarrow \cos \phi$ $=0$

3. C
The graph of $f(x)=\operatorname{Aoox}(\omega x$ ' $\varphi)$ is symmetric with respect to the origin $\Leftrightarrow$ the graph of $f(x)$ passes through the origin $\Leftarrow \cos \phi$ $=0$