Question

If cos x = -4/5 and tan x > 0, the value of sin x is

Answer 1

Observation #1:  if the tangent is + then x must be in Quadrant I or III.

Observation #2:  If the cosine is - then x must be in Quadrant II or III.

Thus, we know for certain that x must be in Quadrant III.  In Quadrant III, the "opposite side" of the angle in question is - and so is "the adjacent side."

Thus, if cos x = -4/5, the adj side is -4, the hyp is 5 and from the Pythagorean Theorem we know that the opp side is 3:  3^2 + (-4)^2 = 5^2.

Thus, sin x = opp / hyp = -3/5 (Answer d).