Q. 17 - 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. 

$r=1-\cos \theta$

Step-by-Step Solution

Answer

The graph of the equation is:

Step 1. Given information

The equation of the curve:

$r=1-\cos \theta$

Step 2. Graph the equation in θ r -plane.

The value of $\theta$ lies on the horizontal axis and $r$ lies on the vertical axis.

The graph of $r=1-\cos \theta$ is obtained by reflecting the graph of $r=\cos \theta$ then shifting the graph by 1 unit, vertically upward.

Here the graph shows the value of $r$ in all four quadrant when graph is plotted in the polar plane.