Question

for the question graph r = cos 5Θ + n cos Θ, 0 ≤ Θ ≤ π For the integers n = -5 to n = 5.

Does this mean that -5,-4,-3,-2,-1,0,1,2,3,4, and 5 are all on the same graph?

I really do not understand polar graphs any help would be much appreciated.

Answer 1

I think they want you to use a separate graph for each of the values of n to show what happens to the graph as n changes.
Wolfram might be of help here:
Just change the values in front of the 2nd term to see how it affects the graph.
I have shown the graph for n = 3

http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+cos+5%CE%98+%2B+3+cos+%CE%98

interesting to play around with it.