Question

Graph the cardioids$r=1+\sin \theta andr=1-\sin \theta$. What is the relationship between these two graphs?

Short answer

Both the graphs intersect each other at certain points.

Step-by-step solution

Step 1. Given Information.

The given curves are $r=1+\sin \theta andr=1-\sin \theta$.

Step 2. Graphically

The equations will be as :

$r=1+a\sin \theta$

Both the graph intersect each other at certain points. Changing the value of $a$changes the size of the cardioid but does not affect its shape. The larger the value of $a$, the larger the resulting cardioid.

The graphs of a given curve are :