bongamin12
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A curve c has parametric equations x=sec^2(t)+1, y=2sin(t), -pi/4<=t<=pi/4
Show that a Cartesian equation of c is y=√[(8-4x)/(1-x)] for a suitable domain which should be stated.

How do you rearrange this?
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bongamin12
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A curve c has parametric equations x=sec^2(t)+1, y=2sin(t), -pi/4<=t<=pi/4
Show that a Cartesian equation of c is y=√[(8-4x)/(1-x)] for a suitable domain which should be stated.
How do you rearrange this?
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RDKGames
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(Original post by bongamin12)
A curve c has parametric equations x=sec^2(t)+1, y=2sin(t), -pi/4<=t<=pi/4
Show that a Cartesian equation of c is y=√[(8-4x)/(1-x)] for a suitable domain which should be stated.
How do you rearrange this?
Note that \sec^2 t can be written in terms of \cos^2 t, which can be written in terms of \sin^2 t, which can be written in terms of y. Hence eliminating the paramter t between the two equations.
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bongamin12
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(Original post by RDKGames)
Note that \sec^2 t can be written in terms of \cos^2 t, which can be written in terms of \sin^2 t, which can be written in terms of y. Hence eliminating the paramter t between the two equations.
I've tried rearranging for cos^2(t)+sin^2(t) = 1 which got me:
(1/x-1)+(y/2)^2=1
However i rearragned this to get y=√[(4x-8)/(x-1)]
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RDKGames
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(Original post by bongamin12)
I've tried rearranging for cos^2(t)+sin^2(t) = 1 which got me:
(1/x-1)+(y/2)^2=1
However i rearragned this to get y=√[(4x-8)/(x-1)]
Same thing. Note that

\dfrac{a}{b} = \dfrac{-a}{-b}.
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bongamin12
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(Original post by RDKGames)
Same thing. Note that

\dfrac{a}{b} = \dfrac{-a}{-b}.
Oh I should've been writing 1 as (-x-1)/(-x-1) correct ?
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RDKGames
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(Original post by bongamin12)
Oh I should've been writing 1 as (-x-1)/(-x-1) correct ?
No what I mean is that

\dfrac{4x-8}{x-1} = \dfrac{-(4x-8)}{-(x-1)}
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bongamin12
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(Original post by RDKGames)
No what I mean is that

\dfrac{4x-8}{x-1} = \dfrac{-(4x-8)}{-(x-1)}
Oh ok I understand now. because it is a common factor.Thank you for the help ! I'll remember to look out for common factors better next time.
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David Getling
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Two general points. To be well prepared to tackle parametric equations you need to be very good at working with trig identities. Most students struggle quite a bit with these, so LOTS of practice with them is essential.

When you are asked to sketch a parametric curve, having a graphics display calculator can be a real godsend. Both the Casio fx-cg50 and the TI-Nspire CX will do a great job. They will also really help in many others ways that have nothing to do with graphs (eg. finding critical regions for hypothesis testing with binomial distributions).
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