Determine the subintervals of the interval $\displaystyle 0 \le \theta \le 2\pi$ where the function $\displaystyle r=cos(2\theta)$ is either increasing or decreasing. Label these intervals I, II, III,...

To determine pole values set $\displaystyle r=0$

$\displaystyle 0=cos(2\theta) \rightarrow cos^{-1}0=2\theta \rightarrow \theta = \frac{cos^{-1}0}{2}$

$\displaystyle \theta= \frac{\pi}{4} , \frac{\pi}{2} , \frac{3\pi}{4} , \pi , \frac{5\pi}{4} , \frac{3\pi}{2} , \frac{7\pi}{4} , 2\pi$

$\displaystyle \theta = 0 , r=1$

$\displaystyle \theta = \frac{\pi}{4} , r=0$

$\displaystyle \theta = \frac{\pi}{2} , r=-1$

$\displaystyle \theta = \frac{3\pi}{4} , r=0$

$\displaystyle \theta = \pi , r=1$

$\displaystyle \theta = \frac{5\pi}{4} , r=0$

$\displaystyle \theta = \frac{3\pi}{2} , r=-1$

$\displaystyle \theta = \frac{7\pi}{4} , r=0$

$\displaystyle \theta = 2\pi , r=1$

Now I'm supposed to sketch a graph and this is the part I'm confused about. All the examples we did before had $\displaystyle \theta = 0 , r=0$ to start with, so I'm not really sure how to start when $\displaystyle \theta=0 , r=1$. This part is confusing me. Novice to this stuff.