The Student Room Group
Reply 1
devesh254
This is from P3 June 03 Edexcel Paper:

1. The curve C is described by the parametric equations

x = 3cost y = cos2t

0 (less than and equal to) t (less than or equal to) pi

(a) Find a cartesian equation of the curve C.
(b) Draw a sketch of the curve C.


I should be fine with (b)...it's (a) that I'm not sure about...

thanks in advance!



x=3cost can be rearranged as cost=x/3.
y=cos2t = 2(cost)^2 - 1
y = 2(x/3)^2 - 1
y= 2(x^2/9) - 1
y = (2x^2 / 9) -1
Reply 2
Gaz031
x=3cost can be rearranged as cost=x/3.
y=cos2t = 2(cost)^2 - 1
y = 2(x/3)^2 - 1
y= 2(x^2/9) - 1
y = (2x^2 / 9) -1


ah gaz mate...thanks (again)...

just one more thing...i found themark scheme...it says for (b) there is a restricted domain of -3<x<3

can someone please exaplain why? thanks!
Reply 3
x = 3cost, from the parametric equations, and you know that -1<cost<1.
Reply 4
dvs
x = 3cost, from the parametric equations, and you know that -1<cost<1.


damn lol why cant i work it out...

so how do you find out this domain? can you please show me step by step? sorry for being a pain!

thanks in advance!
Reply 5
It should be -1<cos<1, sorry...
At minimum cos, x=3(-1)=-3, and at maximum cos, x=3(1)3. So -3<x<3.