I see that there is a more or less similar question in the list, but my one is not a duplicate. I will be grateful if you take a look at how I try to approach the task, and help me to find my mistakes - I am still struggling to get to grips with sketching polar graphs on xy-plane. Important: the goal is to do that "by hand", namely, first sketch the fundamental cycle of the polar graph on $r\theta$ plane, and then manually (and logically - here is one of my main problems) transfer it to the xy-plane.
Please, tell me which of the two approaches I shall follow, as I am a bit confused.
(1.1) Do I correctly choose values for $\theta$ and do I then correctly compute values of the fundamental cycle of the $r = cos(5\theta)$?
(please, see the image below)
(1.2) Then, based on those values, do I correctly compute x and y coordinates to plot the graph on xy-plane?
But this looks not right to me. Eventually I need to get this:
(2) On the other hand, according to graphing rules, if (x) is multiplied by a certain value, then the its value is "shrieked" by that value, namely we need to divide all original x-s by that value; in this case by 5. But how it is supposed to work in this case when I manually need to first find values of r, and then using them to find x and y values?
Thank you very much!