precalculus: Identify the graph and the polar equation

Question

Identify the graph and the polar equation. r = 4 sin (2 theta)

Answer 1

In (θ,r) space this is a sinusoid with amplitude 4 and period π, so in (x,y) space it creates 4 lobes as θ passes from 0 to 2π, with r > 0 lobes in quadrants I and III and r < 0 lobes in quadrants IV and II. The overall graph is like a 4-bladed pinwheel.

Answer 2

The graph of the equation is a four-leaf rose. Examples should be in your text book.