If tan(x) = -3, and x is in quadrant II, then we can use the Pythagorean identity to find the value of sin(x):
sin^2(x) + cos^2(x) = 1
tan^2(x) + 1 = sec^2(x)
(-3)^2 + 1 = sec^2(x)
10 = sec^2(x)
sec(x) = sqrt(10)
cos(x) = 1 / sec(x) = 1 / sqrt(10)
sin(x) = tan(x) * cos(x) = -3 / sqrt(10)
Now, we can use the double-angle identities to find sin(2x), cos(2x), and tan(2x):
sin(2x) = 2 sin(x) cos(x) = 2 (-3 / sqrt(10)) (1 / sqrt(10)) = -6 / 10 = -0.6
cos(2x) = cos^2(x) - sin^2(x) = (1 / 10) - (-9 / 10) = 10 / 10 = 1
tan(2x) = (2 tan(x)) / (1 - tan^2(x)) = (2 (-3)) / (1 - (-3)^2) = 6 / 8 = 3 / 4
Therefore, sin(2x) = -0.6, cos(2x) = 1, and tan(2x) = 3/4.