SOLUTION: Find all the solutions between 0 and 2pi to the equation cos(2x)=sin(x)+1

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Question 378203: Find all the solutions between 0 and 2pi to the equation
cos(2x)=sin(x)+1

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi,
Find all the solutions between 0 and 2pi to the equation
cos(2x)=sin(x)+1
cos+2%28theta%29 = 1 - 2sin^2%28theta%29
1 - 2sin^2(x) = sin (x) + 1
2sin^2(x) + sin (x) =0
sin(x)[2sin(x) + 1] = 0
sin(x)=0
x = 0,pi
2sin(x) + 1 = 0
sin(x) = -1/2
x = 7/6 pi, 11/6 pi
(cos(x), sin(x))