document.write( "Question 544717: If sin(x) + cos(x) = 2/3,
\n" ); document.write( "then find the value of sin(2x). \n" ); document.write( "

Algebra.Com's Answer #355213 by reviewermath(1029) $\"\"$ $\"About$

You can put this solution on YOUR website!
Square both sides of the first equation, the result is
\n" ); document.write( " $\"sin%5E2%28x%29%2B2%2Asin%28x%29%2Acos%28x%29%2Bcos%5E2%28x%29=4%2F9\"$
\n" ); document.write( " $\"%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29%2B2%2Asin%28x%29%2Acos%28x%29=4%2F9\"$ , use the Pythagorean Identity $\"sin%5E2%28x%29%2Bcos%5E2%28x%29=1\"$ , the result is
\n" ); document.write( " $\"1%2B2%2Asin%28x%29%2Acos%28x%29=4%2F9\"$ , use the double angle formula $\"sin%282x%29+=+2sin%28x%29%2Acos%28x%29\"$ , the result is
\n" ); document.write( " $\"1%2Bsin%282x%29=4%2F9\"$
\n" ); document.write( "Therefore $\"highlight%28sin%282x%29=-5%2F9%29\"$ \n" ); document.write( "

\n" );