Polar Curves r>=0 Watch

Y12_FurtherMaths
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Please can someone explain why the mini curve drawn inside the larger curve disappears when r becomes >=0? Because I thought it would remain since it doesn’t occur within the regions when r is negative according to the graph of y=2+4cos3theta. Question 3bi
https://imgur.com/a/KVkNVj8
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mqb2766
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The graph at the top of the page is similar to what you should get, but some of the tangents etc are a bit different.
The mini loop(s) you seem to be talking about occur when
r = 2+4cos(3theta) < 0
which occurs in the three intervals like (2pi/9,4pi/9) ... and the mini loops have a (negative) length of 2
I don't know why you believe they should remain as they're excluded by the question. The 3 loops with a length of 6 are what you want?

(Original post by Y12_FurtherMaths)
Please can someone explain why the mini curve drawn inside the larger curve disappears when r becomes >=0? Because I thought it would remain since it doesn’t occur within the regions when r is negative according to the graph of y=2+4cos3theta. Question 3bi
https://imgur.com/a/KVkNVj8
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Y12_FurtherMaths
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(Original post by mqb2766)
The graph at the top of the page is similar to what you should get, but some of the tangents etc are a bit different.
The mini loop(s) you seem to be talking about occur when
r = 2+4cos(3theta) < 0
which occurs in the three intervals like (2pi/9,4pi/9) ... and the mini loops have a (negative) length of 2
I don't know why you believe they should remain as they're excluded by the question. The 3 loops with a length of 6 are what you want?
Sorry I’m a bit confused. I’ve provide pictures of what the curves look like on my imgur post (there’s 3 pictures). I thought when you change the curve to make r>=0 any part of your original curve that lies between those tangents goes away which is why I’m confused since you’ll see that they lie inside the larger curve so I wasn’t sure why you’d remove them. And how do you know they have a negative length? Sorry if this doesn’t make sense I’m just really confused
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mqb2766
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I missed the other pictures when I originally replied, but the post is still ok.
r = 2+4cos
r must be negative when cos is less than -1/2. This occurs in three intervals.
The lowest r can be is -2, which corresponds to the length of these smaller curves
(Original post by Y12_FurtherMaths)
Sorry I’m a bit confused. I’ve provide pictures of what the curves look like on my imgur post (there’s 3 pictures). I thought when you change the curve to make r>=0 any part of your original curve that lies between those tangents goes away which is why I’m confused since you’ll see that they lie inside the larger curve so I wasn’t sure why you’d remove them. And how do you know they have a negative length? Sorry if this doesn’t make sense I’m just really confused
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Y12_FurtherMaths
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(Original post by mqb2766)
I missed the other pictures when I originally replied, but the post is still ok.
r = 2+4cos
r must be negative when cos is less than -1/2. This occurs in three intervals.
The lowest r can be is -2, which corresponds to the length of these smaller curves
I’m still confused because those mini loops don’t occur in the intervals?
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mqb2766
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They do, can you give a point?
(Original post by Y12_FurtherMaths)
I’m still confused because those mini loops don’t occur in the intervals?
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Y12_FurtherMaths
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(Original post by mqb2766)
They do, can you give a point?
This is how I see it
https://imgur.com/a/2hNZFaA
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mqb2766
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Yes, but when r is negative you go in the opposite direction.
So the part when r is negative in quadrant 1 actually shows itself as the miniloop in quadrant 3.
(Original post by Y12_FurtherMaths)
This is how I see it
https://imgur.com/a/2hNZFaA
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Y12_FurtherMaths
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(Original post by mqb2766)
Yes, but when r is negative you go in the opposite direction.
So the part when r is negative in quadrant 1 actually shows itself as the miniloop in quadrant 3.
Will that be the same for all curves with mini loops then? They will disappear if we set r>=0?
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mqb2766
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For this (type of) problem, yes. There will be a smooth tangent at 0.
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Y12_FurtherMaths
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(Original post by mqb2766)
For this (type of) problem, yes. There will be a smooth tangent at 0.
Ok thanks for your help
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