Trig

Tan theta 12/5 ,pi <theta<3pi/2
Find sin 2theta

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  1. 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

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    posted by drwls

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