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# fp2 polar coordinates watch

1. 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?
2. (Original post by cooldudeman)
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
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.

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?
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.
3. (Original post by ghostwalker)
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.
thanks, not really that tough to remember so i don't mind.

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Updated: March 9, 2013
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