CPM Homework Help : PC3 Problem 13-158

Determine the points of intersection for the polar curves $r=2\sin\left(2θ\right)$ and $r=2\cos\left(θ\right)$ .

Step 1:

Set the equations equal to each other (because $r = r$ ).

Step 2:

Divide both sides by $2$ .

Step 3:

Apply the Double Angle Identity for sine.

Step 4:

Set the equation equal to $0$ and factor.

Step 5:

Use the Zero Product Property to solve for $θ.$

Step 6:

Use your values for $θ$ to solve for $r$ .