Question 1174752
you are given that tan(theta) = 4/3.


to find the angle, solve for arctan(4/3) using your calculator.
you will find that arctan(4/3) = 53.13010235 degrees.


that's the angle in the first quadrant.
the equivalent angle in the third quadrant is 180 + 53.13010235 = 233.13010235 degrees.


you are now looking for sin(2 * theta) when theta = 233.13010235 degrees.
2 * theta = 466.2602047 degrees.
you get sin(2 * 233.13010235) = sin(466.2602047)) = .96.
that should be your answer.


if you used the sin(2 * theta) identity, you would have gotten:
sin(2 * theta) = 2 * sin(theta) * cos(theta) which becomes:
sin(2 * theta) = 2 * sin(233.13010235) * cos(233.13010235) = .96.


that's the same as we got before, so it should be good.