Trig
posted by Stacey grahaM .
Tan theta 12/5 ,pi <theta<3pi/2
Find sin 2theta

Think of a 5,12,13 right triangle. The principle angle (to the y axis) is arcsin 12/13
Theta is in the third quadrant, and therefore
theta = pi + arcsin 12/13
sin 2theta = 2 sin theta cos theta
= 2*(12/13)(5/13) = 120/169 = 0.71006
Check: theta = 4.31760 radians
2 theta = 8.6352 radians
sin (2 theta) = 0.71006