SOLUTION: Determine all solutions of the given equation. Express in radians. 2(cosx)^2-sinx-1=0 Im having trouble getting the equation to the same trig function throughout and factoring.

Algebra ->  Trigonometry-basics -> SOLUTION: Determine all solutions of the given equation. Express in radians. 2(cosx)^2-sinx-1=0 Im having trouble getting the equation to the same trig function throughout and factoring.      Log On


   

Question 863454: Determine all solutions of the given equation. Express in radians.
2(cosx)^2-sinx-1=0
Im having trouble getting the equation to the same trig function throughout and factoring. Please help!
Found 2 solutions by Alan3354, lwsshak3:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Determine all solutions of the given equation. Express in radians.
2(cosx)^2-sinx-1=0
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Sub 1+-+sin%5E2%28x%29+for+cos%5E2%28x%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Determine all solutions of the given equation. Express in radians.
2(cosx)^2-sinx-1=0
***
2cos%5E2%28x%29-sin%28x%29-1=0
2%281-sin%5E2%28x%29%29-sin%28x%29-1=0
2-2sin%5E2%28x%29-sin%28x%29-1=0
-2sin%5E2%28x%29-sin%28x%29%2B1=0
-2sin^2(x)-sin(x)+1=0
2sin^2(x)+sin(x)-1=0
(2sin(x)-1)(sin(x)+1)=0
..
sin(x)=1/2
x=π/3+2πn, 5π/3+2πn, n=integer
or
sin(x)=-1
x=2π/3+2πn, n=integer