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# Polar coordinates help watch

1. I was doing FP2 and something interesting occurrd to me. When you have say r=sin2feta then the graph has four loops but when it's r=sin3feta there's only 3 loops why is it Luke this? And can anyone give me the proof about it? Also what about r=asin(bfeta) when b is not an integer. Thanks.
2. (Original post by Ultimate1)
I was doing FP2 and something interesting occurrd to me. When you have say r=sin2feta then the graph has four loops but when it's r=sin3feta there's only 3 loops why is it Luke this? And can anyone give me the proof about it? Also what about r=asin(bfeta) when b is not an integer. Thanks.
Actually, thats because I think as far as A level is concerned we only consider +ve values of r. If you remove this restriction and let r be -ve as well you'll get 6 loops.

Edit: After thinking I realised that if r is neg then actually the even ones will have 1/2 as many loops. I think in FP2 you only consider r to be +ve though.
3. (Original post by anshul95)
Actually, thats because I think as far as A level is concerned we only consider +ve values of r. If you remove this restriction and let r be -ve as well you'll get 6 loops.
This is not true. graphing r=sin(3 theta) will give you 3 closed loops, not 6.

OP, try investigating it for yourself using Wolfram Alpha

eg http://www.wolframalpha.com/input/?i...n%283+theta%29

Try it where b is odd or even, then try fractional values of b.
Try to think about the graph of sin(b*x) and what's going on here.
4. (Original post by Ultimate1)
I was doing FP2 and something interesting occurrd to me. When you have say r=sin2feta then the graph has four loops but when it's r=sin3feta there's only 3 loops why is it Luke this? And can anyone give me the proof about it? Also what about r=asin(bfeta) when b is not an integer. Thanks.
As far as FP2 is concerned r = sin(2 theta) will only give 2 loops due to the restriction that A2 courses place with respect to r greater than or equal to zero..

You see 4 loops when you allow the r values to be negative.
now with r = sin (3 theta) .. one could argue that there are "6 loops" but that the loops obtained from negative r values lie on top of the 3 loops that FP2 syllabi consider to be valid ...
5. (Original post by StephenNeill)
This is not true. graphing r=sin(3 theta) will give you 3 closed loops, not 6.

OP, try investigating it for yourself using Wolfram Alpha

eg http://www.wolframalpha.com/input/?i...n%283+theta%29

Try it where b is odd or even, then try fractional values of b.
Try to think about the graph of sin(b*x) and what's going on here.
oh....my FP2 book went through drawing r=sin(3theta) and missed out the bits were sin(3theta) were negative. i.e. it only considered 0<theta<pi/3 and
2pi/3<theta<pi and 4pi/3<theta<5pi/3. The other ranges give -ve r. Can you explain to me what why I am wrong (which looking at Wolfram I clearly am)? Is it because -ve r is intepreted in some way I am not familiar with?

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