Question

If sin x = -3/5 and cos x > 0 what is the value of tan x​

Answer 1

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.