Question

Find all solutions in the interval [0, 2π]:

sin(x/2) = 1 - cosx

Answer 1

What I have is:
x=0, π, π/3, 5π/3--but I'm unsure about the latter two answers.

Answer 2

x = 2 pi n
x = 4 pi n + pi/3
x = 4 pi n + (5 pi)/3
for n in Z
Check the attached image

Answer 3

Haha, well using graphing technology or graphs isn't permitted but that does help verify my answers, I suppose. Thanks!

Answer 4

hey
hold it i got it, im gonna send u a pic with the equations and stuff

Answer 5

Ah, cool, do our answers match up or am I wrong?

Answer 6

I'm assuming the latter if you're sending me a picture of a sol'n, lol

Answer 7

You have cos(x)=1-2sin^2(x/2)


sin(x/2) = 1 - cosx
sin(x/2)=2sin^2(x/2)
sin(x/2)(1-2sin(x/2)=0
sin(x/2)=0 or sin(x/2)=1/2

Answer 8

Mhm, thanks.

Answer 9

yw