1. ## Graphing Polars

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.

2. It would be extremely hard to instruct graphing in polar coordinates via a post. You may want to see your prof or talk to someone who can physical do it with you.

3. Originally Posted by dwsmith
It would be extremely hard to instruct graphing in polar coordinates via a post. You may want to see your prof or talk to someone who can physical do it with you.
Could you then confirm that what I drew is correct?

I drew 4 circles. A circle connecting (0,0) and (1,0) ; (0,0) and (-1,0) ; (0,0) and (0,1) ; (0,0) and (0,-1).