How do I make x=sin(t)t and y=cos(2t) Cartesian?

Question

I have

x=sin(t)

y=cos(2t)

Can anyone show me a step by step process to make these into Cartesian equations? I know that it is y=-2x^2+1, but I want to know how to arrive to that.

Answer 1

use double angle formula of cosine .. . .

y = cos(2t) = 1 - 2sin²(t)

thus y = 1 - 2x^2

Answer 2

Sin(t) = x  from (1)

from  2

y = Cos(2t)

y = 1 -2(sint)^2 =1 - 2x^2

or

y = 1 - 2x^2