In this problem, we want to determine the graph of a polar equation.
We are given the following polar equation:
[tex]r=4\sin2\theta[/tex]
The general form for this polar equation is a rose curve:
[tex]r=a\sin n\theta[/tex]
We know the following rules:
• When n is an even number, there are 2n petals
,
• The value of a gives us the length of the petals.
Since we are working with a sine function, the petals will not aline with the x and y axis, as the sine function begins at the origin.
So we know the following:
[tex]\begin{gathered} r=4\sin2\theta \\ \\ a=4 \\ \\ n=2 \end{gathered}[/tex]
The length of our petals is 4 units, and there will be a total of 4 petals.
Here's the graph:
