Show that the curve with vector equation is the curve of intersection of the surfaces and . Use this fact to sketch the curve.

I am completely lost.

Would i take $\displaystyle z = 2sin(t)$ and plug it into

$\displaystyle x^2 + y^2 + z^2 = 4$

$\displaystyle x^2 + y^2 + (2sin(t))^2 = 4$

then

$\displaystyle x^2 + y^2 + (4sin^2(t)) = 4$

I dont know what to do.