Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. sin(u) = −3/5, 3𝜋/2 < u < 2𝜋

Answer 1

3π/2 < u < 2π, so this is the fourth quadrant, with positive cos

sin(u) = -3/5, so cos is 4/5 (If a side is length 3 and the hypotenuse is 5, the other side is length 4)

sin(2u) = 2 sin(u)cos(u) = 2 (-3/5)(4/5) = -24/25

cos(2u) = 2 cos²(u) -1 = 2(4/5)² - 1 = 32/25- 1 = 7/25

tan(2u) = sin(2u)/cos(2u) = -24/25/(7/25) = -24/7