We can use the following trigonometric identity to solve for the value of sin(theta):
sin^2(theta) + cos^2(theta) = 1
Since we know that sec(theta) = -5/12, we can use the reciprocal identity of secant:
sec(theta) = 1/cos(theta)
-5/12 = 1/cos(theta)
cos(theta) = -12/5
Since sin(theta) > 0 and cos(theta) < 0 (because -12/5 is negative), we know that theta is in the second quadrant.
Now, we can use the Pythagorean identity of sine and cosine in the second quadrant:
sin^2(theta) = 1 - cos^2(theta)
sin^2(theta) = 1 - (-12/5)^2
sin^2(theta) = 1 - 144/25
sin^2(theta) = 25/25 - 144/25
sin^2(theta) = -119/25
Since sine is positive in the second quadrant, we take the positive square root of 119/25 and get:
sin(theta) = sqrt(119)/5
Therefore, sin(theta) = sqrt(119)/5 and theta is in the second quadrant.