Q. 20 - Calculus

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.   

$r=\sin 2\theta$

Step-by-Step Solution

Answer

The graph of the equation is:

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.