Find the exact values ​​of sin 2u, cos 2u, and tan 2u using the double angle formulas.

Question

1. sin u = 3/5, 0 <u <π / 2

Answer 1

sinu =3/5

cosu = 4/5

sin2u = 2sinucosu = 2(12/25) = 24/25

cos2u = cos^2u - sin^2u = 16/25 - 9/25 = 7/25

tan2u = sin2u/cos2u =(24/25)/(7/25) = 24/7

use an inverse trig function on a calculator to check the answers

u = about 37 degrees

2u = about 74 degrees

sin74 = 0.96 = 24/25

cos74 =0.28 = 7/25

tan74 = 3.43 = 24/7