SOLUTION: what are all the solutions of 2cos^2(x)-cos(x)-1=0 that lie in the interval [0, 2pi]
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Question 561942: what are all the solutions of 2cos^2(x)-cos(x)-1=0 that lie in the interval [0, 2pi]
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Do a simple substitution. Let )
Then
\ -\ \cos(x)\ -\ 1\ =\ 2u^2\ -\ u\ -\ 1\ =\ 0)
It factors
(2u\ +\ 1)\ =\ 0)
So
or
Hence
\ =\ 1)
or
\ =\ -\frac{1}{2})
So
)
or
)
Find these values on the unit circle:
bearing in mind that the cosine is represented by the 
-coordinate of a point on the unit circle and don't miss the fact that your given interval is inclusive of BOTH end points.
John
My calculator said it, I believe it, that settles it
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