document.write( "Question 935570: Find the exact value for cos2x given sinx = √2/2? \n" ); document.write( "

Algebra.Com's Answer #568808 by josmiceli(19441) $\"\"$ $\"About$

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Divide top and bottom by $\"+sqrt%28+2+%29+\"$
\n" ); document.write( " $\"+sqrt%282%29+%2F+2+=+1+%2F+sqrt%28+2+%29+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( " $\"+sin%28+x+%29+=+a%2Fc+\"$
\n" ); document.write( "label the components:
\n" ); document.write( " $\"+a%2Fc+=+1%2Fsqrt%282%29+\"$
\n" ); document.write( "Find the horizontal component
\n" ); document.write( " $\"+b%5E2+=+c%5E2+-+a%5E2+\"$
\n" ); document.write( " $\"+b%5E2+=+%28sqrt%282%29%29%5E2+-+1%5E2+\"$
\n" ); document.write( " $\"+b%5E2+=+2+-+1+\"$
\n" ); document.write( " $\"+b%5E2+=+1+\"$
\n" ); document.write( " $\"+b+=+1+\"$
\n" ); document.write( " $\"+b+=+-1+\"$
\n" ); document.write( "---------------
\n" ); document.write( " $\"+cos%28x%29+=+b%2Fc+\"$
\n" ); document.write( " $\"+cos%28+x+%29+=+1%2Fsqrt%282%29+\"$
\n" ); document.write( " $\"+x+=+pi%2F4+\"$
\n" ); document.write( "and, also
\n" ); document.write( " $\"+cos%28+x+%29+=+-1%2Fsqrt%282%29+\"$
\n" ); document.write( " $\"+x+=+3pi%2F4+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( " $\"+2x+=+pi%2F2+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+2x+=+3pi%2F2+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "Finally,
\n" ); document.write( " $\"+cos%28+2x+%29+=+0+\"$
\n" ); document.write( "In both of these cases\r
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