Question

A rose curve is graphed on a polar coordinate grid. It has 8 loops or petals each with a length of 9 units. The loops are rotated at an angle off of the polar axis.
Question
Use the graph to answer the question.
Write the equation for the graph of the rose curve.
(1 point)
Responses

r = 4 sin 9θ
r = 4 sin 9 θ

r = 8 sin 9θ
r = 8 sin 9 θ

r = 9 sin 4θ
r = 9 sin 4 θ

r = 9 sin 8θ
r = 9 sin 8 θ
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Answer 1

To find the correct equation for the rose curve, we can use the general form for a rose curve given in polar coordinates:

- \( r = a \sin(n\theta) \) or \( r = a \cos(n\theta) \)

Where:
- \( a \) is the length of each petal,
- \( n \) determines the number of petals.

**Key Points to Note:**
1. For a rose curve:
- If \( n \) is odd, the number of petals is \( n \).
- If \( n \) is even, the number of petals is \( 2n \).

In this case, we know there are 8 petals, which means \( n \) should be 4 (since \( 2n = 8 \) gives \( n = 4 \)).

Additionally, the length of each petal is given as 9 units, meaning \( a = 9 \).

Thus, the correct form of the equation should be:
\[ r = 9 \sin(4\theta) \]

The correct response from the choices given is:
**r = 9 sin 4θ**.