Polar Coordinates - Geometric Reasoning

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beachpanda
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#1
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Hi - I've attached an explanation from my Further Maths book which I'm unsure about.

Methods 1 & 2 I'm fine with, but as for Method 3 I'm not sure what exactly this proves? I'm fine with OPA being a right-angled triangle but from the line "Using trigonometry, r = 10cos(theta) as required...." onwards I'm not sure what's going on?

Can anyone help?

Edit: I've tried reuploading but the website keeps rotating the images
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Lucifer323
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(Original post by beachpanda)
Hi - I've attached an explanation from my Further Maths book which I'm unsure about.

Methods 1 & 2 I'm fine with, but as for Method 3 I'm not sure what exactly this proves? I'm fine with OPA being a right-angled triangle but from the line "Using trigonometry, r = 10cos(theta) as required...." onwards I'm not sure what's going on?

Can anyone help?

Edit: I've tried reuploading but the website keeps rotating the images
Hi, in method 2 you convert from polar form to Cartesian form and get the equation of the circle.

In method 3 you do the same thing from a geometrical perspective.

It's not very clear what they intend to do.
Last edited by Lucifer323; 1 year ago
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beachpanda
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(Original post by Lucifer323)
Hi, in method 2 you convert from polar form to Cartesian form and get the equation of the circle.

In method 3 you do the same thing from a geometrical perspective.

It's not very clear what they intend to do.
Yeah I'm not really sure either. I get the geometry but not sure what's happening after that.

Anyone able to help?
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davros
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(Original post by beachpanda)
Yeah I'm not really sure either. I get the geometry but not sure what's happening after that.

Anyone able to help?
It's just a wordy geometrical argument rather than an actual algebraic proof.

They're just showing you that if you start off with a circle as described but choose your origin of (polar) coordinates to be the point on the left edge of the circumference, then as a point moves round the circle it is always true that  r = 10\cos\theta with the choice of r and \theta that they have defined.
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Lucifer323
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(Original post by beachpanda)
Yeah I'm not really sure either. I get the geometry but not sure what's happening after that.

Anyone able to help?
What question do you have?

It's better if you present the question here and I can have a look at.
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beachpanda
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(Original post by davros)
It's just a wordy geometrical argument rather than an actual algebraic proof.

They're just showing you that if you start off with a circle as described but choose your origin of (polar) coordinates to be the point on the left edge of the circumference, then as a point moves round the circle it is always true that  r = 10\cos\theta with the choice of r and \theta that they have defined.
Right I seeeeeee, didn't realise they were proving that the length of r is 10cos(theta). Got it, thanks
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