Find the vertical tangents of the below polar curve. \[ r=3 \cos \theta, 0 \leq \theta \leq \pi \] a. $\theta=0, \frac{\pi}{2}$ b. $\theta=\frac{\pi}{2}, \pi$ c. $\theta=0, \frac{\pi}{2}, \pi$ d. $\theta=\frac{\pi}{4}, \frac{3 \pi}{4}$

Step 1 ：Given the polar curve \(r=3 \cos \theta, 0 \leq \theta \leq \pi\)

Step 2 ：The vertical tangents of a polar curve occur when the derivative of the function is undefined or infinite. In polar coordinates, the derivative of the function is given by \(\frac{dr}{d\theta}\). We need to find the values of \(\theta\) for which this derivative is undefined or infinite.

Step 3 ：Let's find the derivative of the function \(r\) with respect to \(\theta\): \(\frac{dr}{d\theta} = -3\sin(\theta)\)

Step 4 ：The vertical tangents of the polar curve occur at \(\theta=0\) and \(\theta=\pi\). This is because the derivative of the function is zero at these points, indicating a vertical tangent.

Step 5 ：Final Answer: The vertical tangents of the polar curve \(r=3 \cos \theta, 0 \leq \theta \leq \pi\) occur at \(\theta=0\) and \(\theta=\pi\). So, the correct answer is \(\boxed{\text{c. } \theta=0, \frac{\pi}{2}, \pi}\).