Question

Graphing Polar Equations Sketch a graph of the polar equation.

$r=-3\cos \theta$= .

Short answer

The graph of the polar equation $r=-3\cos \theta$ is

Step-by-step solution

Step 1. Given information.

The given polar equation $r=-3\cos \theta$.

Step 2.The graph of the polar equation.

Firstly, we will find the values of, at the different values ofand convert the polar form into rectangular form by formula$\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$to get the points and then using those points.

Polar equation is$r=-3\cos \theta$

Put $\theta =0$

We get $r=-3$

Substituting the values in $\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$

We get$\begin{array}{l}x=-3\\ y=0\end{array}$

Similarly, put $\theta =\frac{\pi }{4}$

We get $r=3$

Substituting the values in $\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$

We get $\begin{array}{l}x=2.1213\\ y=2.1213\end{array}$

Similarly, we get more values as $\begin{array}{l}x=3\\ y=0\end{array}$

And $\begin{array}{l}x=0\\ y=\pm 3\end{array}$

Similarly, we get more points.