Question

Graphing Polar Equations

Use a graphing device to graph the polar equation. Choose the domain $\theta$ to make sure you produce the entire graph$r=\sqrt{1-0.8{\sin }^2\theta }$

(hipped)

Short answer

The graph of the given polar equation is-

Step-by-step solution

Step 1. Given information

A polar equation is given as $r=\sqrt{1-0.8{\sin }^2\theta }$

Step 2. Concept used

For sketching the graph, first, find different values r for different$\theta$. After that, convert them into x and y by using equations-

$\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$

To convert rectangular to polar coordinates use formulas-

$\begin{array}{l}r=\sqrt{x^2+y^2}\\ \tan \theta =\frac{y}{x}\end{array}$

Once we have the points draw a graph by plotting them.

Step 3. Calculation

The polar equation is given as$r=\sqrt{1-0.8{\sin }^2\theta }$,

Consider the domain $\theta$as $0\le \theta \le 2\pi$

Plot the points on graph-