# Arslan

• April 9th 2013, 02:00 PM
arslan9451
Arslan
Can we determine the number of leaves in a given trigonometric function for which we have to plot a graph in polar coordinates...? For Example, sin(3theeta) has 3 leaves and cos(2theeta) has 4 leaves etc....Is there any formula ?
• April 9th 2013, 06:37 PM
Soroban
Re: Arslan
Hello, arslan9451!

Quote:

Can we determine the number of leaves in a given trigonometric function
. . for which we have to plot a graph in polar coordinates?
For example, $\sin3\theta$ has 3 leaves, and $\cos2\theta$ has 4 leaves etc.
Is there any formula ?

If you are referring to "rose curves": . $\begin{Bmatrix}r \:=\: a\sin n\theta \\ \text{or} \\ r \:=\:a\cos n\theta\end{Bmatrix}$ .there is a formula.

If $n$ is odd, there are $n$ petals.

If $n$ is even, there are $2n$ petals.