Question

Families of Polar Equations

These exercises involve families of polar equations

Graph the family of polar equations $r=1+c\sin 2\theta$ for $\text{n=1,2,3,4\&5}$. How is the number of loops related n ?

Short answer

The graph of the given polar equation is-

Step-by-step solution

Step 1. Given information

A polar equation is given as $r=1+c\sin 2\theta$

Step 2. Concept used

First, draw graphs individually for each value n . There will be five graphs, then merge them for the final answer.

Step 3. Calculation

The graph for$n=1$,

$r=1+0.3\sin 2\theta ,0\le \theta \le 2\pi$

The graph for $n=2$,

$r=1+0.6\sin 2\theta ,0\le \theta \le 2\pi$

The graph for n=3 ,

$r=1+\sin 2\theta ,0\le \theta \le 2\pi$

The graph for n=4 ,

$r=1+1.5\sin 2\theta$

The graph for n=5 ,

$r=1+2\sin 2\theta ,0\le \theta \le 2\pi$