Answer:
tan x = opp / adj = -3/4
Step-by-step explanation:
If sin x = -3/5, then we have the following info as a starting point:
opposite side = -3 (implying that the angle is in either QIII or QIV), and
hypotenuse = 5.
Using the Pythagorean Theorem, we find that x² + (-3)² = 5², where x is the length of the adjacent side. Solving for x², we get x² = 25-9 = 16, so that the adj. side, x, is either +4 or -4.
If cos x > 0, then x must be in either QI or QIV.
If both conditions are satisfied (sin x = -3/5 and cos x > 0), then the angle x must be in QIV.
Then tan x = opp / adj = -3/4.
