Help eliminating parameters?

Question

I've tried the trig identities (mainly sin^2(x) + cos^2(x) = 1), but I'm still stumped on this problem.

x = cos(2t), y = sin(2t), 0<=t<=pi

After using the double angle formulas, I get this:
x = cos^2(t) - sin^2(t), y = 2sin(t)cos(t)
But I'm lost as to how to combine these.

Answer 1

the 2t is an irrelevance. say u = 2t 0<=u<2pi
and you just have x = cosu, y = sin u

which you eliminate with x^2 + y^2 = 1 ... the unit circle as you should have expected.

Answer 2

The first you tried is OK
x^2+y^= sin^2(2t) +cos^2(2t)=1
so x^2+y^2=1 with y>=0

Answer 3

x^2= cos^(2t)
y^2= sin^2(2t)
x^2+y^2 = cos^2(2t) + sin^2(2t)
x^2+y^2 = 1
It's the unit circle.

Answer 4

x = cos(2t) ........ x² = cos² (2t)
y = sin(2t) ......... y² = sin² (2t)

x² + y² = cos² (2t) + sin² (2t) = 1
x² + y² = 1
the unit circle, since 0 ≤ 2t ≤ 2π.