Q. 47 - Calculus

Question

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

Step-by-Step Solution

Answer

Both the graphs intersect each other at certain points.

Step 1. Given Information.

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

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 :