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

Mathematics

1 answer:

r-ruslan [8.4K]4 years ago

6 0

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).

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