Question

Families of Polar Equations

These exercises involve families of polar equations

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

Short answer

The graph of given polar equation is-

Step-by-step solution

Step 1. Given information

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

Step 2. Concept used

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

Step 3. Calculation

The graph for$n=1$,

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

The graph for$n=2$,

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

The graph for$n=3$,

$r=1+\sin 3\theta ,0\le \theta \le 2\pi$

The graph for ,

$n=4$$r=1+\sin 4\theta ,0\le \theta \le 2\pi$

The graph for$n=5$ ,

$r=1+\sin 5\theta ,0\le \theta \le 2\pi$