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.

$r=1+\sin 3\theta$

Short answer

The graph of the equation:

Step-by-step solution

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.