parametric equation help (1 Viewer)

[osak23]

find the cartesian equation of the curve where the parametric equations are:


x=cost2t
y=cost

(eliminate the 't' in other words)

 

[deswa1]

Use double angles on x:
x=2cos^2t-1
Square y:
y^2=cos^2t
Sub into the first equation I wrote:
x=2y^2-1

 

[Nooblet94]

Just thought I'd make that a bit nicer to read:

<a href="http://www.codecogs.com/eqnedit.php?latex=\\ x=\cos 2t=2\cos^2t-1~~~~~(1)\\ y=\cos t\\ \therefore y^2=\cos^2 t~~~~~~~~~~~~~~~~~~~~(2)\\ \textrm{Subbing (2) into (1):}\\ x=2y^2-1" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\\ x=\cos 2t=2\cos^2t-1~~~~~(1)\\ y=\cos t\\ \therefore y^2=\cos^2 t~~~~~~~~~~~~~~~~~~~~(2)\\ \textrm{Subbing (2) into (1):}\\ x=2y^2-1" title="\\ x=\cos 2t=2\cos^2t-1~~~~~(1)\\ y=\cos t\\ \therefore y^2=\cos^2 t~~~~~~~~~~~~~~~~~~~~(2)\\ \textrm{Subbing (2) into (1):}\\ x=2y^2-1" /></a>