Question 825715
I'm going to use x in place of θ


sin(x) = 4/5


sin^2(x) = 16/25 ... square both sides


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sin^2(x) + cos^2(x) = 1


16/25 + cos^2(x) = 1


cos^2(x) = 1 - 16/25


cos^2(x) = 25/25 - 16/25


cos^2(x) = (25 - 16)/25


cos^2(x) = 9/25


cos(x) = -sqrt(9/25) ... we are in quadrant II, so cos(x) < 0


cos(x) = -3/5


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sin(2x) = 2*sin(x)*cos(x)


sin(2x) = 2*(4/5)*(-3/5)


sin(2x) = (2/1)*(4/5)*(-3/5)


sin(2x) = (2*4*(-3))/(1*5*5)


sin(2x) = -24/25


Final Answer: sin(2x) = <font color="red">-24/25</font>