Question
find the exact value of sinu/2, given that cosu=-4/5 and pi/2less than u less than pi
Answers
Reiny
use the formula
cos 2A = 1 - 2sin^2 A
cos u = 1 - 2sin^2 (u/2) , π/2 < u < π , so u is in quad II
-4/5 = 1 - 2sin^2 (u/2)
2 sin^2 (u/2) = 9/5
sin^2 (u/2) = 9/10
sin u/2 = √(9/10)
= 3/√10 or 3√10/10
cos 2A = 1 - 2sin^2 A
cos u = 1 - 2sin^2 (u/2) , π/2 < u < π , so u is in quad II
-4/5 = 1 - 2sin^2 (u/2)
2 sin^2 (u/2) = 9/5
sin^2 (u/2) = 9/10
sin u/2 = √(9/10)
= 3/√10 or 3√10/10