Question

Graphing Polar Equations Sketch a graph of the polar equation.

$r=3\sin \theta$.

Short answer

The equation $r=3\sin \theta$ can be graphed as

Step-by-step solution

Step 1. Given information.

Given: The polar equation is $r=3\sin \theta$

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$r=3\sin \theta$

In general form, it can be written as$r=2a\sin \theta$

Thus, it is a circle.
Let us assume values $\theta$ from 0 to and summarise the values r in the table below.

Step 3. Using the above table, we can draw the graph as