sin (x/2) = 1- cosx solve for interval (0 2π)

Question

sin (x/2) = 1- cosx solve for interval (0 2π)

algebraic means without a calculator 

Answer 1

Hi Morgan,

 

sin(x/2) = 1 - cosx

cos(x) = 1 - 2sin^2(x/2)  (this is an identity) 

sin(x/2) = 1 - (1 - 2sin^2(x/2))

sin(x/2) = 1 - 1 + 2sin^2(x/2)

sin(x/2) = 2sin^2(x/2)

let sin(x/2) = u

u = 2u^2

u = 1/2

sin(x/2) = 1/2

x = 60 and 300 degrees in the interval (0, 2pi)