how do i set this problem up?

Find tan (s + t) given that sin s = 1/4, with s in quadrant 2, and sin t = -1/2, with t in quadrant 4.

To find tan (s + t), you can use the formula for the tangent of the sum of two angles:

tan (s + t) = (tan s + tan t) / (1 - tan s * tan t)

To set up the problem, follow these steps:

1. Determine the values of sin s and sin t given in the problem.
- Given that sin s = 1/4, in quadrant 2, this means that the opposite side of the angle s is 1, and the hypotenuse is 4. To find the adjacent side, you can use the Pythagorean theorem. Since the adjacent side is negative in quadrant 2, you can take the negative square root: adj s = -√(4^2 - 1^2) = -√15.

- Given that sin t = -1/2, in quadrant 4, this means that the opposite side of the angle t is -1, and the hypotenuse is 2. To find the adjacent side, you can use the Pythagorean theorem. Since the adjacent side is positive in quadrant 4, you can take the positive square root: adj t = √(2^2 - (-1)^2) = √3.

2. Calculate the values of tan s and tan t.
- tan s = opposite side / adjacent side = 1 / (-√15) = -√15/15

- tan t = opposite side / adjacent side = -1 / √3 = -√3/3

3. Substitute the values of tan s and tan t into the formula for tan (s + t).
- tan (s + t) = (tan s + tan t) / (1 - tan s * tan t)
- tan (s + t) = (-√15/15 + (-√3/3)) / (1 - (-√15/15 * -√3/3))
- Simplify the expression:
= (-√15 - √3) / (1 + (√15 * √3) / 15)
= (-√15 - √3) / (1 + √45/15)
= (-√15 - √3) / (1 + √3/√5)
= (-√15 - √3) / (1 + √3/√5) * (√5/√5)
= (-√15√5 - √3√5) / (√5 + √3)
= (-√75 - √15) / (√5 + √3)

Therefore, the expression for tan (s + t) is (-√75 - √15) / (√5 + √3).

First you have to find what s and t equal. Then you can find tan(s + t)