I had a more or less similar question, and I marked it as solved, because at that moment it was indeed solved - I was correctly advised and explained how to proceed. So this question is not a duplicate, and it refers more to computations than to the polar equation $r=\cos(5\theta)$ per se.
My goals is to learn how to pick angles in the given range, and then compute r, x, y, which should be go smoothly, I assume, once I have correct angles.
Please, advice me and help me to understand once and for all my mistakes, as I do unexpectedly struggle with finding correct values of $\theta$, and thus $r$, $x$ and $y$, in the range $[-π/5 , π/5]$ - that is I don't understand if I pick correct values from $[-π/5,0]$, and from $[0$ to $π/5]$. I find that values don't seem to form anything close to the beautiful rose, which $r=\cos(5\theta)$ represents.
Here is a screen shot from excel table to show only the beginning of my computations.
EDIT: I have changed the picture because I had a typo in the previous one.
Thank you very much!