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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).

The value of sin x=-3/5

We have the observe that if the tangent is positive  then x must be in Quadrant I or III.

Also, If the cosine is - then x must be in Quadrant II or III.

Thus, we know for the given  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 and the hypotenuse  is 5.

What is the Pythagorean theorem?

We know that the Pythagorean theorem

[tex]side^{2} +side^{2} =hypotenuse^{2}[/tex]

so by using the Pythagorean formula we get,

 [tex]3^2 + (-4)^2 = 5^2.[/tex]

Therefore we have,

[tex]sin x = opp / hyp = -3/5[/tex]

Therefore the option d is correct.

To learn more about the trigonometry visit:

https://brainly.com/question/24349828

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