# Parametric Equation

• August 4th 2010, 11:57 PM
heatly
Parametric Equation
Eliminate t in the following equations to determine the type of curve represented.

x = cos t , y= 1 - cos 2t

I have so far managed to reduce the y=1-cos2t equation to 0 ? ,by using the addition formula and subing in x,to get rid of t.........but the ans is y= 2(1-x^2) ,-1<x<1.
• August 5th 2010, 12:04 AM
Prove It
Remember that $\cos{2t} = 2\cos^2{t} - 1$.

So $y = 1 - \cos{2t}$

$= 1 - (2\cos^2{t} - 1)$

$= 1 - 2\cos^2{t} + 1$

$= 2 - 2\cos^2{t}$

$= 2 - 2x^2$.

I think you can see that this is a Quadratic, and since $x = \cos{t}$ and $-1 \leq \cos{t} \leq 1$ for all $t$, that means $-1 \leq x \leq 1$.
• August 5th 2010, 12:14 AM
heatly
Thanks for that Prove It