Q. 24 - 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.    

$r=1+\sin 3\theta$

Step-by-Step Solution

Answer

The graph of the equation:

Step 1. Given information.

The equation of the curve: 

$r=1+\sin 3\theta$

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  $r=1+\sin 3\theta$ is obtained by compressing the  the graph of $r=\sin \theta$  by factor $\frac{1}{3}$ horizontally, then vertically shift the graph by $1$ unit upward.