Where is trigonometric function in negative?

Answer 1

In the domain [0, 2*pi],sin is negative for pi < x < 2*pi

cos is negative pi/2 < x < 3*pi/2 and

tan is negative for pi/2 < x < pi and 3*pi/2 < x < pi.

Also, the same applies for all intervals obtained by adding any integer multiple of 2*pi to the bounds.