document.write( "Question 106799This question is from textbook Precalculus with limits
\n" ); document.write( ": Find all values of \"x\" within the interval [0,2pi) for the equation:
\n" ); document.write( "cos(x/2)= $\"+sqrt%282%29+\"$ /2
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Algebra.Com's Answer #77742 by Fombitz(32388) $\"\"$ $\"About$

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Since,
\n" ); document.write( " $\"cos%28%28x%2F2%29%29=+sqrt%282%29%2F2\"$
\n" ); document.write( "You know from the relationship,
\n" ); document.write( " $\"sin%5E2%28y%29%2Bcos%5E2%28%28y%29%29=1\"$
\n" ); document.write( " $\"sin%5E2%28x%2F2%29%2B1%2F2=1\"$
\n" ); document.write( " $\"sin%28x%2F2%29=sqrt%282%29%2F2\"$
\n" ); document.write( "As you can see on the unit circle, there are two angles (A and -A) that solve the equation,
\n" ); document.write( " $\"cos%28%28x%2F2%29%29=+sqrt%282%29%2F2\"$
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\n" ); document.write( "You can determine A several ways.
\n" ); document.write( "Two ways are using the inverse trigonometric functions and geometrically.
\n" ); document.write( "Using inverse trig, the only angle that has equal sine and cosine is 45 degrees, or
\n" ); document.write( " $\"A=45%5Eo\"$
\n" ); document.write( " $\"x%2F2=45%5Eo\"$
\n" ); document.write( " $\"x=90%5Eo\"$
\n" ); document.write( " $\"-A=45%5Eo\"$
\n" ); document.write( " $\"x%2F2=-45%5Eo\"$
\n" ); document.write( " $\"x=-90%5Eo\"$
\n" ); document.write( "Geometrically, the triangle with A as one angle is a right tringle. It is also an right, isoceles triangle with a hypotneuse of 1 and sides of $\"sqrt%282%29%2F2\"$
\n" ); document.write( "Therefore A+A=90 or A=45. \n" ); document.write( "

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