How can I parametrize Viviani's Curve? 
How can I parametrize Viviani's Curve ?
$\textbf{Viviani’s curve}$ is the intersection of the unit sphere with center $(\frac{-1}{2},0,0)$ and the cylinder with center $(0,0,0)$ and radius $1/2$

Paramatrization of the cylinder is
$(\frac{1}{2}cos(t),\frac{1}{2}sin(t),?)$
and the unit sphere
$(cos(\theta)cos(\phi)-\frac{1}{2},cos(\theta)sin(\phi),sin(\theta))$
I think, i have to use some trigonometric equations but i see only 1 in this case.

Let $a=1/2$.
The sphere is given by $(x+a)^2+y^2+z^2=1$ and the cylinder is given by $x^2+y^2=a^2$.
As you have noticed, the cylinder gives $x=a\cos t$, $y=a\sin t$. Plug these into the sphere and get:
$$
1 = (x+a)^2+y^2+z^2 = a^2+2a^2\cos t + a^2\cos^2 t + a^2\sin^2 t + z^2 = 2a^2(1+\cos t)+z^2
$$
Now solve for $z$ using that $a=1/2$. You may want to look up the half-angle formula.
