If cos x = -4/5 and tan x > 0, the value of sin x is a) 3/5 b) 5/3 c) -5/3 d) -3/5

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).

answer: i ! the answer is   9000 seconds, also d

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-lavira : )

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