We want to plot a graph of ;
[tex]r=2\cos (2\theta)[/tex]
Using the formula;
[tex]r=a\cos (n\theta)[/tex][tex]\begin{gathered} \text{Where a}\ne0 \\ \text{and } \\ n\text{ is an integer }>1 \end{gathered}[/tex]
The graph will have the rose form.
And if the value of n is odd, the rose will have n petals, if the value of n is even, the rose will have 2n petals;
For the given question;
n = 2 (even)
So, the rose will have;
[tex]\begin{gathered} 2n=2(2) \\ =4\text{ petals} \end{gathered}[/tex]
The graph is shown below;
