# How do you graph r=3-2costheta?

Aug 1, 2018

See the graph of this dimpled limacon.

#### Explanation:

$0 \le r = 3 - 2 \cos \theta \in \left[1 , 5\right]$

Period = period of $\cos \theta = 2 \pi$.

Using $r = \sqrt{{x}^{2} + {t}^{2}} \mathmr{and} \cos \theta = \frac{x}{r}$,

the Cartesian form is obtained as

${x}^{2} + {y}^{2} - 3 \sqrt{{x}^{2} + {y}^{2}} = 2 x = 0$

The graph of this dimpled limacon is immediate.

graph{ x^2 + y^2 -3sqrt ( x^2 + y^2 )+ 2x = 0[-20 20 -10 10]}