Suppose that sinθ=8/17 and θ is in the second quadrant. Find sin (2θ), cos (2θ), and tan (2θ) exactly.

sin (2Θ) = 2cosΘsinΘ

sinΘ=opposite/hypotenuse=8/17

adjacent = (17^2 - 8^2) ^1/2 = 15

sin (2Θ) = 2cosΘsinΘ = 2 * (15/17) * (8/17) = 240/289

opposite of 2Θ equals 240

hypotenuse of 2Θ equals 289

adjacent of 2Θ = (289^2 - 240^2) ^1/2 = 161

cos (2Θ) = 161/289

tan (2Θ) = 240/161