SOLUTION: Solve for theta 0 degrees < theta < 360 degrees. Sin(theta/2)+cos(theta)=1

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Question 770559: Solve for theta 0 degrees < theta < 360 degrees. Sin(theta/2)+cos(theta)=1
Found 2 solutions by solver91311, lwsshak3:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


on the interval

Half angle formula:

Substitute:



Isolate the radical



Square both sides:



Plain ol' algebra:



Factor the quadratic:



Hence, or

Check the unit circle: or.

But , therefore:

or

John

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Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for theta 0 degrees < theta < 360 degrees. Sin(theta/2)+cos(theta)=1
***
sin(x/2)+cosx=1
sin(x/2)=±√((1-cosx)/2)
sin(x/2)=1-cosx
√((1-cosx)/2)=1-cosx
square both sides
(1-cosx)/2=1-2cosx+cos^2x
1-cosx=2-4cosx+2cos^2x
2cos^2x-3cosx+1=0
(2cosx-1)(cosx-1)=0
..
2cosx-1=0
cosx=1/2
x=π/3, 5π/3
..
cosx-1=0
cosx=1
x=0