Question

the equation $r = 3\cos(6\theta)$ represents a rose curve. how many petals does the graph contain?
3
6
12
18

Explanation:

Step1: Recall rose - curve formula

The polar equation of a rose - curve is \(r = a\cos(n\theta)\) or \(r=a\sin(n\theta)\).

Step2: Determine number of petals rule

If \(n\) is even in \(r = a\cos(n\theta)\) or \(r=a\sin(n\theta)\), the number of petals is \(2n\). If \(n\) is odd, the number of petals is \(n\).

Step3: Identify \(n\) value

In the equation \(r = 3\cos(6\theta)\), \(n = 6\) (which is even).

Step4: Calculate number of petals

Using the rule for even \(n\), the number of petals is \(2n\). Substitute \(n = 6\) into \(2n\), we get \(2\times6=12\).

Answer:

C. 12