document.write( "Question 881000: sin(4x)cos(3x)+cos(4x)sin(3x)=0.51
\n" ); document.write( "solve by finding exact values for two fundamental solutions.
\n" ); document.write( "

Algebra.Com's Answer #531862 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "sin(4x)cos(3x)+cos(4x)sin(3x)=0.51\r\n" );
document.write( "\r\n" );
document.write( "Use the identity\r\n" );
document.write( "\r\n" );
document.write( "\"sin%28alpha%2Bbeta%29\" \"%22%22=%22%22\" \"sin%28alpha%29%2Acos%28beta%29\"\"%22%22%2B%22%22\"\"cos%28alpha%29%2Asin%28beta%29\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute \"alpha=4x\", \"beta=3x\":\r\n" );
document.write( "\r\n" );
document.write( "\"sin%284x%2B3x%29\" \"%22%22=%22%22\" \"sin%284x%29%2Acos%283x%29\"\"%22%22%2B%22%22\"\"cos%284x%29%2Asin%283x%29\"\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "\"sin%287x%29\" \"%22%22=%22%22\" \"sin%284x%29%2Acos%283x%29\"\"%22%22%2B%22%22\"\"cos%284x%29%2Asin%283x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"sin%287x%29\" \"%22%22=%22%22\" \"0.51\"\r\n" );
document.write( "\r\n" );
document.write( "The right side equals to 0.51.  \r\n" );
document.write( "\r\n" );
document.write( "Take inverse sines of both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"7x\" \"%22%22=%22%22\" sin-1(0.51) + \"2pi%2An\"\r\n" );
document.write( "\r\n" );
document.write( "also\r\n" );
document.write( "\r\n" );
document.write( "\"7x\" \"%22%22=%22%22\" (\"pi\" - sin-1(0.51) + \"2n%2Api\")\r\n" );
document.write( "\r\n" );
document.write( "\"7x\" \"%22%22=%22%22\" -sin-1(0.51) + \"%282n%2B1%29pi%29\")\r\n" );
document.write( "Therefore, solving for x in each\r\n" );
document.write( "\r\n" );
document.write( "\"x\" \"%22%22=%22%22\" \"1%2F7\"sin-1(0.51) + \"2pi%2An%2F7\"\r\n" );
document.write( "\r\n" );
document.write( "also\r\n" );
document.write( "\r\n" );
document.write( "\"x\" \"%22%22=%22%22\" \"-1%2F7\"sin-1(0.51) + \"%282n%2B1%29pi%2F7%29\")\r\n" );
document.write( "\r\n" );
document.write( "To get the two fundamental solutions let n=0 in each:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"x\" \"%22%22=%22%22\" \"1%2F7\"sin-1(0.51)\r\n" );
document.write( "\r\n" );
document.write( "and\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"x\" \"%22%22=%22%22\" \"-1%2F7\"sin-1(0.51) + \"pi%2F7%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );