Question

Graphing Polar Equations Sketch a graph of the polar equation.

$r=\sin 4\theta$

Short answer

The graph of the polar equation $r=4\sin \theta$is

Step-by-step solution

Step 1. Given information.

The polar equation$r=\sin 4\theta$ .

Step 2.The graph of the polar equation.

Firstly, we will find the values of , at the different values of 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$r=\sin 4\theta$.

Put $\theta =0$ , we get

r=0

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

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

Similarly, put $\theta =\frac{\pi }{8}$

r=1

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

We get $\begin{array}{l}x=0.9238\\ y=0.3826\end{array}$

Similarly, we get more points.