What is the domain of the function f(x) = sqrt[cos x].

For y = f(x), the domain of the function f(x) is all the
values of x for which y is real.

Here y = f(x) =
sqrt[cos(x)]

The value of cos x lies in the interval [-1,
1] for all values of x.

But sqrt [cos(x)] is real only when
cos(x) is not negative. Also it has to be kept in mind that cos(x) is a periodic
function and we get the same value for cos x after x has decreased on increased by
2*pi.

The interval for x where the value of cos x is not
negative is [0 + 2*n*pi, pi/2 + 2*n*pi] U [3*pi/2 + 2*n*pi, 0 +
2*n*pi]

The domain of the function f(x) =
sqrt[cos(x)] is [0 + 2*n*pi, pi/2 + 2*n*pi] U [3*pi/2 + 2*n*pi, 0 +
2*n*pi]