Question

Graphing Polar Equations Sketch a graph of the polar equation

$r=-3(1+\sin \theta )$.

Short answer

The equation $r=-3(1+\sin \theta )$can be graphed as.

Step-by-step solution

Step 1. Given information.

The given polar equation is $r=-3(1+\sin \theta )$.

Step 2. The graph of the polar equation.

We will find the general form of the given equation. Then using the inferences drawn from it, we will draw the graph.

The given polar equation is$r=-3(1+\sin \theta )$.

In general form, it can be written as$r=a(1\pm \sin \theta )$

Thus, it is a cardioid.

Step 3. It can be graphed as.