Answer
$$f(\theta)=\sin \left(2\left(\theta-\frac{\pi}{2}\right)+\pi\right)+2,\ \ \ \ \ \ [0,2\pi]$$
Work Step by Step
We are given the function:
$$f(\theta)=\sin \left(2\left(\theta-\frac{\pi}{2}\right)+\pi\right)+2,\ \ \ \ \ \ [0,2\pi]$$
We sketch the function over the given interval as shown below.
