SOLUTION: Find all real numbers in the interval[0,2π) that satisfy the equation √2cos(x/2)-1=0.
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Question 760334: Find all real numbers in the interval[0,2π) that satisfy the equation √2cos(x/2)-1=0.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
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The angles that have a cosine value of are in the first and fourth quadrant.
is a solution in the first quadrant
That gives us:
-->
The next fist quadrant solution to the equation is
--> which is not in the interval [,)
is a fourth quadrant solution to
and so are all angles differing by a multiple of
That makes a solution to
However, --> which is not in the interval [,).
SO the only solution in the interval [,) is .
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