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 ?

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- Apr 9th 2013, 02:00 PMarslan9451Arslan
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 ?

- Apr 9th 2013, 06:37 PMSorobanRe: 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, $\displaystyle \sin3\theta$ has 3 leaves, and $\displaystyle \cos2\theta$ has 4 leaves etc.

Is there any formula ?

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

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

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