document.write( "Question 760334: Find all real numbers in the interval[0,2π) that satisfy the equation √2cos(x/2)-1=0. \n" ); document.write( "

Algebra.Com's Answer #462627 by KMST(5328) $\"\"$ $\"About$

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$\"sqrt%282%29cos%28x%2F2%29-1=0\"$ --> $\"cos%28x%2F2%29=1%2Fsqrt%282%29=sqrt%282%29%2F2\"$
\n" ); document.write( "The angles that have a cosine value of $\"1%2Fsqrt%282%29=sqrt%282%29%2F2\"$ are in the first and fourth quadrant.
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\n" ); document.write( " $\"x%2F2=pi%2F4\"$ is a solution in the first quadrant
\n" ); document.write( "That gives us:
\n" ); document.write( " $\"x%2F2=pi%2F4\"$ --> $\"highlight%28x=pi%2F2%29\"$
\n" ); document.write( "The next fist quadrant solution to the equation is
\n" ); document.write( " $\"x%2F2=pi%2F4%2B2pi=9pi%2F4\"$ --> $\"x=9pi%2F2%3E2pi\"$ which is not in the interval [ $\"0\"$ , $\"2pi\"$ )
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\n" ); document.write( " $\"x%2F2=-pi%2F4\"$ is a fourth quadrant solution to $\"sqrt%282%29cos%28x%2F2%29-1=0\"$
\n" ); document.write( "and so are all angles differing by a multiple of $\"2pi\"$
\n" ); document.write( "That makes $\"x%2F2=-pi%2F4%2B2pi=7pi%2F4\"$ a solution to $\"sqrt%282%29cos%28x%2F2%29-1=0\"$
\n" ); document.write( "However, $\"x%2F2=7pi%2F4\"$ --> $\"x=7pi%2F2%3E2pi\"$ which is not in the interval [ $\"0\"$ , $\"2pi\"$ ).
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\n" ); document.write( "SO the only solution in the interval [ $\"0\"$ , $\"2pi\"$ ) is $\"highlight%28x=pi%2F2%29\"$ .
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