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.

$r=\frac{1}{2}-\sin \theta$

Short answer

The graph of the equation is:

Step-by-step solution

Step 1. Given information

The equation:

$r=\frac{1}{2}-\sin \theta$

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 $r=\frac{1}{2}-\sin \theta$is obtained by reflecting the graph of $r=\sin \theta$with respect to the horizontal axis, then shifting the graph by $\frac{1}{2}$unit, vertically upward.