Question

Graphing Polar Equations Sketch a graph of the polar equation.

$r=2\sin 5\theta$.

Short answer

The graph of the polar equation $r=2\sin 5\theta$is

Step-by-step solution

Step 1. Given information.

The given polar equation $r=2\sin 5\theta$

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.

The polar equation is$r=2\sin 5\theta$.

Put $\theta =\frac{\pi }{10}$.

We getr=2

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

We get $\begin{array}{l}x=1.9021\\ y=0.6180\end{array}$

Put $\theta =\frac{\pi }{2}$

We get $r=2$

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

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

Similarly, we get more points.