Question

Graph the equation in the θr-plane. Label each arc of your curve with the quadrant in which the corresponding polar graph will occur.

$r=\sin 2\theta$

Short answer

The graph of the equation is:

Step-by-step solution

Step 1. Given information

The equation of the curve:

$r=\sin 2\theta$

Step 2. Graph the equation in θr-plane. 

The value of $\theta$lies on the horizontal axis and $r$lies on the vertical axis.

The graph of $r=\sin 2\theta$ is obtained by compressing the the graph of $r=\sin \theta$by factor of $\frac{1}{2}$horizontally.