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given tan theta= 1/2, pi<theta<3 pi/2 find sin 2 theta
|dw:1358913683596:dw| First off, theta is in 3rd quadrant. So sin theta is negative, cos theta is negative Tan theta = 1/2 so by the triangle, sin theta = -1/sqrt(5), cos theta = -2/sqrt(5) NOTE: sin (2x) = 2sin(x)cos(x) sin(2 theta) = 2 * (-1/sqrt(5)) * (-2/sqrt(5)) = 4/5