FP1 polar coordinates - does anyone know how to draw graphs for these???? Watch

minnie
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Hi

I've been revising polar coordinates for the FP1 exam on Monday, and if you are asked to draw r = acos2Θ when r > 0, what should it look like? When I do it on my calculator it has four 'petals', but I thought that when Θ = pi/2 you wouldn't draw anything, as r would be smaller than 0. Could anyone explain whether or not this would be right?

Thanks!!
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IChem
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(Original post by minnie)
Hi

I've been revising polar coordinates for the FP1 exam on Monday, and if you are asked to draw r = acos2Θ when r > 0, what should it look like? When I do it on my calculator it has four 'petals', but I thought that when Θ = pi/2 you wouldn't draw anything, as r would be smaller than 0. Could anyone explain whether or not this would be right?

Thanks!!
Yeah, but when theta = pi/2 you are drawing r=acos(pi) since r=acos 2theta...right.

If you have a graphics calculator, just copy out what you see, nothing more simple! Just make sure that you have set your theta min/max right!
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aster100
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(Original post by minnie)
Hi

I've been revising polar coordinates for the FP1 exam on Monday, and if you are asked to draw r = acos2Θ when r > 0, what should it look like? When I do it on my calculator it has four 'petals', but I thought that when Θ = pi/2 you wouldn't draw anything, as r would be smaller than 0. Could anyone explain whether or not this would be right?

Thanks!!
That's what I thought. Doing it in my head, if r > 0 there would only be petals to the "sides", while if r is anything, there would be 4 petals. :confused: :confused: :confused:
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Audrey Hepburn
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I buy a calculator that does it for me :soc:
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JohnnySPal
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In polar co-ordinates you're required ot have r>0 (as you say). So if r is negative you just don't draw it, because the graph isn't defined there. Simple as that. (I think :p:)

Get it on a graphical calculator (or online, if a website will plot it? Try Google?) and verify that the shape you're drawing is in fact correct.
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minnie
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(Original post by aster100)
That's what I thought. Doing it in my head, if r > 0 there would only be petals to the "sides", while if r is anything, there would be 4 petals. :confused: :confused: :confused:
Yeh that's exactly what's confusing me! Even when Θ = pi/2 and therefore cos2Θ is cos(pi) then r will still be smaller than zero.... I don't have a clue what I'm going to do in the exam if this comes up!
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silent ninja
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How are you doing these? Look at r as theta goes from 0 to \frac{\pi}{4}, then 2\theta goes from 0 to \frac{\pi}{2}, and r goes from a to 0. Draw half a 'petal' from a to 0 over this range.
Do the same for \frac{\pi}{4} to  \frac{\pi}{2} as cos2\theta goes from 0 to -1 and so r from 0 to -a, and so on... you'll notice a pattern as you do these and will be able to draw them quickly.

For your question, look at the region  \frac{5 \pi}{4} to  \frac{3 \pi}{2} , you'll notice r goes from 0 to -a and this corresponds on a sketch to the region  \frac{\pi}{4} to  \frac{ \pi}{2}. So there is a 'petal' here.
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aster100
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(Original post by silent ninja)
How are you doing these? Look at r as theta goes from 0 to \frac{\pi}{4}, then 2\theta goes from 0 to \frac{\pi}{2}, and r goes from a to 0. Draw half a 'petal' from a to 0 over this range.
Do the same for \frac{\pi}{4} to  \frac{\pi}{2} as cos2\theta goes from 0 to -1 and so r from 0 to -a, and so on... you'll notice a pattern as you do these and will be able to draw them quickly.

For your question, look at the region  \frac{5 \pi}{4} to  \frac{3 \pi}{2} , you'll notice r goes from 0 to -a and this corresponds on a sketch to the region  \frac{\pi}{4} to  \frac{ \pi}{2}
So how many petals will there be?
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silent ninja
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(Original post by aster100)
So how many petals will there be?
4.

Remember that -a means you are going in the reverse direction for that length.
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Wish
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If a question like this is given:

Sketch the curve with polar equation r=a\cos 3 \theta, a>0, for 0\le\theta\le\pi.

Do we only draw the top half. (Above initial line?)
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aster100
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(Original post by silent ninja)
4.

Remember that -a means you are going in the reverse direction for that length.
OK thanks again
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trickz
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(Original post by IChem)
If you have a graphics calculator, just copy out what you see, nothing more simple! Just make sure that you have set your theta min/max right!
How do you set the min/max? I have a casio fx-9750G
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IChem
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Try the manual. I have a TI-83+. Sorry.
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browser
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(Original post by IChem)
If you have a graphics calculator, just copy out what you see, nothing more simple!
"Undefined variable"....i assume they mean "a"

any help...

edit: and by "they", I of course mean the intergalactic forces that are trying to make me fail this test
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