Identify the type of rose and graph it for the following polar equation: \( r = 3 \cos(2\theta) \)

Step 1 ：The rose is specified by the polar equation \( r = a \cos(n \theta) \) or \( r = a \sin(n \theta) \), where \(a\) is the length of the petal and \(n\) is the number of petals if \(n\) is even or twice the number of petals if \(n\) is odd.

Step 2 ：From the given polar equation, \( r = 3 \cos(2\theta) \), we can identify \(a = 3\) and \(n = 2\). So, this is a rose with 2 petals and each petal has a length of 3.

Step 3 ：To graph this rose, we plot points for various angles \(\theta\) from 0 to \(2\pi\) and connect these points smoothly. The points will trace out two loops, each of radius 3, with one loop for \(0 \leq \theta \leq \pi\) and the other for \(\pi \leq \theta \leq 2\pi\).