Polar Graphs Math Example 3

Follow the full solution, then compare it with the other examples linked below.

medium

How many petals does the rose curve

r = 3\sin(4\theta)

have?

1
For a rose curve $r = a\sin(n\theta)$ or $r = a\cos(n\theta)$ : if $n$ is even, there are $2n$ petals; if $n$ is odd, there are $n$ petals.
2
Here $n = 4$ (even), so the number of petals is $2(4) = 8$ .

Answer

8 \text{ petals}

Rose curves have a petal count that depends on whether

n

is even or odd. When

n

is even, petals appear in both positive and negative

r

directions, doubling the count. Each petal has maximum length

|a| = 3

About Polar Graphs

Graphs of equations in the form $r = f(\theta)$ , producing curves such as rose curves, cardioids, limaçons, and circles in the polar plane.

Describe the graph of [formula] in polar coordinates.

Identify the type of polar curve [formula] and find key features.

Find the area enclosed by one petal of the rose curve [formula].