Problem

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

Answer

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Answer

In our equation, r=5cos⁡(2θ), 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=acos⁡(nθ) or r=asin⁡(nθ), 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=5cos⁡(2θ), 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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