help with pre calc

Question

On the interval  determine which angles are not in the domain of the tangent function, What angles are NOT in the domain of the tangent function on the given interval? _______

Answer 1

The domain of tan(theta) cannot include angles (pi/2) + n x theta because these values make the cos(theta) 0 thus tan(theta) undefined.

Answer 2

tan(θ) = sin(θ)/cos(θ) and since dividing by zero is undefined, we cannot have cos(θ) = 0. Since cos(θ) = 0 at π/2 and 3π/2, those angles are not in the domain of f(θ) = tan(θ).