Question

Graphing Polar Equations Sketch a graph of the polar equation.

$r=2\sin \theta$.

Short answer

The graph of the polar equation $r=2\sin \theta$.

Step-by-step solution

Step 1. Given information.

The given polar equation $r=2+\sin \theta$.

Step 2.The graph of the polar equation.

Firstly, we will find the values of,r at the different values of$\theta$and 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.

The polar equation is$r=2+\sin \theta$.

Put $\theta =0$

We get $r=2$

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

We get $\begin{array}{l}x=2\\ y=0\end{array}$

Similarly, put $\theta =\pi$

We get $r=2$

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

We get $\begin{array}{l}x=-2\\ y=0\end{array}$

Similarly, we get more points.