# OCR C4 Parametric EquationsWatch

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#1
No idea what to do!! It's very irritating...

1) A curve has the parametric equations 'x= asin g' 'y= agcos g'

Where a is a positive constant and range is between (and including) pi to negative pi.

i) Write down the value of g corresponding to the origin, and state the points A and B (y and x intercept respectively of the curve).

ii) Show that dy/dx = -1gtan g and hence find the equation of the tangent to the curve at the origin.

I know how to do part ii) with the right information I just thought I should put it in for context, any help would be great cheers
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13 years ago
#2
I think you have to substitute in x=0 and y=0 to find the value of g but not totally sure what to do. sorry
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#3
No probs cheers for ur thoughts, ne1 else?
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13 years ago
#4
at origin (0,0), g = 0
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#5
How does that give you the two points then? I guess A is (O, pi) but I dunno, what about the second bit? Gah it's all such a pain!
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13 years ago
#6
at origin x = 0 ad y=0 so asing=0 and agcosg = 0 so g has to be 0 at the origin

at A x=0 so asing = 0 so g = 0 (y = 0) or g= pi (y=-pi) or g = -pi (y = pi)

at B y=0 so agcosg = 0 so g=0 (x=0) or g=pi/2 (x=pi) or g=-pi/2 (x = pi/2)

so A = (0,0) or (0,-pi) or (0,pi)
and B=(pi/2,0) or (0,0)
(from the diagram it should be obvious which one is B and which is A)

dy/dx = (dy/dg) / (dg/dy) (chain rule)
= (-agsing + acosg)/ acosg = -gtang + 1 (product rule on agcosg)

at origin g = 0 so dy/dx = 1
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#7
Here's the question in all its printed glory, hope this will help! Thanks for all your help so far by the way it's starting to make sense....
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13 years ago
#8
ive changed my post now hope it makes sence
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#9
Cool yeah cheers, pretty sure I got it, thanks for all you're help, sure it won't be the last time I post a maths question somehow!
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