Problem

Given the polar equation \(r = 5\cos(2\theta)\), identify the graph as a rose and find its number of petals.

Answer

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Answer

In our equation, \(r = 5\cos(2\theta)\), we can see that \(a = 5\) and \(n = 2\). Since \(n\) is even, the number of petals will be twice \(n\).

Steps

Step 1 ：First, we identify the form of the polar equation. Rose curves generally have the form \(r = a\cos(n\theta)\) or \(r = a\sin(n\theta)\), where \(a\) is the length of the petals and \(n\) is the number of petals if \(n\) is odd, or twice the number of petals if \(n\) is even.

Step 2 ：In our equation, \(r = 5\cos(2\theta)\), we can see that \(a = 5\) and \(n = 2\). Since \(n\) is even, the number of petals will be twice \(n\).

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