Question 174693
If cos y = -4/5, then the adjacent side is 4 units and the hypotenuse is 5 units. So the other leg is {{{sqrt(5^2-4^2)=sqrt(25-16)=sqrt(9)=3}}} units. In other words, this triangle has side lengths of 3, 4, and 5 units.



So sin(y) = opposite/hypotenuse = 3/5



Note: sine is positive since 90 < y < 180




So


sin(2y) = 2*sin(y)*cos(y)



sin(2y) = 2*(3/5)*(-4/5) ... Plug in sin(y) = 3/5  and cos y = -4/5



sin(2y) = -24/25