Question

Graphs of Polar Equations Match the polar equation with the graphs labeled I-VI. Use the table on page 519 to help you.

.$r=3\cos \theta$

Short answer

The given equation $r=3\cos \theta$matches with the graph $\text{VI}$.

Step-by-step solution

Step 1.Given information.

A polar equation $r=3\cos \theta$.

Step 2. The correct plot of the equation.

We will plot the given equation and compare it with the graphs given.

Comparing the given equation$r=2a\cos \theta$with , we get,

$\begin{array}{l}2a=3\\ a=1.5\end{array}$

Therefore the given equation corresponds to a circle with a center at coordinates$(1.5,0)$and $(1.5,\frac{\pi }{2})$.

We see that these conditions are met by the graph .$\text{VI}$