First the domain. The domain of sin(x) is all real numbers, so the sin(x) puts no restrictions on the value of x. The next thing to look at is the square root; the argument of a square root can never be negative. But 1 - sin(x) is never negative. So the domain of y is all real numbers.
As far as the tangent line:
I'll leave the task of simplifying this and letting x = 0 to you.
-Dan