Q. 18 - 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.  

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

Step-by-Step Solution

Answer

The graph of the equation is:

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.