If tan(theta)= -1, sin (theta) < 0, and theta is inbetween 0 and 360, then determine the exact value of theta

Question

I understand how to do the question without the "sin0<0". Also I tried to answer the question and I got 0=45 and 0=135.

Answer 1

tan(45^o) = 1 sin(45^o) > 0

tan(135^o) = -1 sin(135^o) > 0

tan(225^o) = 1 sin(225^o) < 0

tan(315^o) = -1 sin(315^o) < 0 Tangent < 0 in quadrants II and IV, sine < 0 in quadrants III and IV, so it's

quadrant IV.