Question

How do you graph `r=5sin5theta`?

Answer 1

I will give you some important points in the first two loops; plot them on polar graph paper:

`|(theta,|,r),(0,|,0),(pi/30,|,2.5),(pi/10,|,5),(pi/6,|,2.5),(pi/5,|,0),((7pi)/30,|,-2.5),((3pi)/10,|,-5),((11pi)/30,|,-2.5),((2pi)/5,|,0)|`

Please understand that there are 5 loops within the domain `0 <= theta < pi` and two of them will give you a negative radius. Plotting any more points beyond this domain will repeat the same loops. I will leave plotting of the 5 loops to you.

Here is the graph to guide you: