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FP3 Polar Curves

A couple harder polar curves questions. I didn't make any useful progress
image.jpg
Can anyone do questions 7 and 8? 7 b ii onwards
(edited 7 years ago)
Reply 1
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Zacken
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Original post by Lucasium
A couple harder polar curves questions. I didn't make any useful progress
image.jpg
Can anyone do questions 7 and 8?


Any specific parts you're stuck on?
the first part of q7 is easier if you reflect the curve in the line y = x ... then it is just a simple integral wrt x. the limits are not hard to find.
Reply 3
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Lucasium
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Original post by Zacken
Any specific parts you're stuck on?


All apart from 7 a and 7bi
Reply 4
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Zacken
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Original post by Lucasium
All apart from 7 a and 7bi


7(b) (ii) is simple a matter of recognising that r2=x2+y2r^2 = x^2 + y^2 and x=rcos⁡θx = r\cos \theta so your equation becomes r2=(2−rcos⁡θ)2r^2 = (2 - r\cos \theta)^2 after which, some re-arranging and simplifying and solving for rr in terms of θ\theta gets you where you need to be.
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Lucasium
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Original post by Zacken
7(b) (ii) is simple a matter of recognising that r2=x2+y2r^2 = x^2 + y^2 and x=rcos⁡θx = r\cos \theta so your equation becomes r2=(2−rcos⁡θ)2r^2 = (2 - r\cos \theta)^2 after which, some re-arranging and simplifying and solving for rr in terms of θ\theta gets you where you need to be.


I tried but only got this farimage.jpg
Reply 6
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Olipoo
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Original post by Lucasium
A couple harder polar curves questions. I didn't make any useful progress
image.jpg
Can anyone do questions 7 and 8?


1=cos(0) from here you can use the (half?) angle formulas that are included in C3 but were most likely not taught in detail.
Reply 7
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Zacken
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Original post by Lucasium
I tried but only got this far


Bit unwieldy?

r2=(2−rcos⁡θ)2⇒±r=2−rcos⁡θ⇒r(cos⁡θ±1)=2⇒r=2cos⁡θ±1r^2 = (2-r\cos \theta)^2 \Rightarrow \pm r = 2-r\cos \theta \Rightarrow r (\cos \theta \pm 1) = 2 \Rightarrow r = \frac{2}{\cos \theta \pm 1}

From which it suffices to see that rr must be positive so you take r=2cos⁡θ+1r = \frac{2}{\cos \theta + 1}
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Lucasium
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Original post by Olipoo
1=cos(0) from here you can use the (half?) angle formulas that are included in C3 but were most likely not taught in detail.


For which question?
Reply 9
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Zacken
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Original post by Lucasium
For which question?


Given that you've repped my post, I take it you've understood - in which case, can you then see how the integral is a multiple of 12∫r2 dθ\frac{1}{2}\int r^2 \, \mathrm{d}\theta which is the area of something you've already found so adjusting for the multiple gets you the required answer.
Reply 10
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Olipoo
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Original post by Lucasium
For which question?


7c
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Lucasium
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Good work guys, I appreciate it. Let's move on to question 8
Reply 12
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Zacken
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Original post by Lucasium
Good work guys, I appreciate it. Let's move on to question 8


Same thing, write x2+3y2=x2+y2+2y2=r2+2(rsin⁡θ)2x^2 + 3y^2 = x^2 + y^2 + 2y^2 = r^2 + 2(r\sin \theta)^2 re-arrange, blah blah.
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Lucasium
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Original post by Zacken
Same thing, write x2+3y2=x2+y2+2y2=r2+2(rsin⁡θ)2x^2 + 3y^2 = x^2 + y^2 + 2y^2 = r^2 + 2(r\sin \theta)^2 re-arrange, blah blah.


These questions are harder than usual aren't they? I haven't had such an issue before
Reply 14
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Zacken
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Original post by Lucasium
These questions are harder than usual aren't they? I haven't had such an issue before


I wouldn't know - I'm not on your exam board, so I'll defer to your judgement.
Reply 15
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Lucasium
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Original post by Zacken
I wouldn't know - I'm not on your exam board, so I'll defer to your judgement.


I've just received news that the booklet is a mix of aqa and MEI, so concern over. It's no excuse but it makes me feel a little better
Original post by Lucasium
I've just received news that the booklet is a mix of aqa and MEI, so concern over. It's no excuse but it makes me feel a little better


Could you link this booklet?
Reply 17
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Lucasium
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Original post by Argylesocksrox
Could you link this booklet?


I suppose I'll take and upload pictures tomorrow, it's a big booklet
Original post by Lucasium
I suppose I'll take and upload pictures tomorrow, it's a big booklet


Thanks mate :biggrin:

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