fp2 polar coordinates

with ones like r=sin(ntheta), it says in my book that it will have n loops, but when i type r=sine(4theta) on wolframalpha, it has 8

and how are we supposed to know how to draw the ones where n is odd? because with the even ones, you just split the loops within the 4 quadrants and draw in a symmetrical way.

also, do exam papers just ask how to sketch the known ones that are shown in textbooks? it seems kinda difficult to just know how to do a sketch and know how it curves...

EDIT: with the odd ones, is it like if its sin, the loop on the right cuts through the positive x-line? and with cos, the bottom loop cuts the negative y-line?

It depends on whether you're allowed negative values of r or not. If you permit negative values then you will get twice the number of loops.



All these are rotationally symmetrical, like a flower with n non-overlapping petals.

Cos is easy, as cos 0 = 1, so one loop has a max value on the positive x-axis.

Sin varies.
If it's of the form 4n+1 then one loop has a max value on the +ve y-axis.
If it's of the form 4n+3 then one loop has a max value on the -ve y-axis.

I doubt they'd expect you to remember these.

Can't comment on what would be on an exam.