Use the given conditions to find the exact values of sin (2u), cos(2u), and tan(2u) using the double-angle formula. sin(u) = - 4/5, 3π/2 < u < 2π

Question

Use the given conditions to find the exact values of sin (2u), cos(2u), and tan(2u) using the double-angle formula.

sin(u) = - 4/5, 3π/2 < u < 2π

Answer 1

We know angle u is in the 4th quadrant, so we know cos u is positive.

We can work out the exact value of cos u (which we need for double angle formulas)

based on the figure below.

sin u = –4/5, cos u = 3/5

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

cos 2u = cos²u – sin²u = (3/5)² – (–4/5)² = (9 –16)/25 = –7/25

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