Question

A curve is given by the parametric equations: `x=cos(t) , y=sin(2t)`, how do you find the cartesian equation?

Answer 1

`y^2=4x^2(1-x^2)`

Explanation:

`x = cos(t)->x^2=cos^2(t)`
`y = sin(2t)=2cos(t)sin(t)->y^2=4cos^2(t)sin^2(t)`

but `cos^2(t)+sin^2(t) = 1`

then

`y^2=4x^2(1-x^2)`