Hello,
A tangent line is horizontal when the derivative is 0 (the derivate number is the slope of the tangent).
So you have to solve for t as you said.
For the derivative of y, let's do it slightly :
We know that :

 the derivative of a constant is 0.

 or here, what's going to interest you is :
 the derivate of cos is sin and the derivate of sin is cos
I think you got all you need here =)
If you still have difficulties show where there is a problem