document.write( "Question 1169221: 8 sin 6x + 8 sin 2x = 0
\n" ); document.write( "I have found the answers pi/2, pi/4+pi/2
\n" ); document.write( "and have failed to get the correct answers when typing them into my homework system (Cengage).
\n" ); document.write( "If anyone can help, I would greatly appreciate it. \n" ); document.write( "

Algebra.Com's Answer #793866 by ikleyn(52943) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "The given equation\r\n" );
document.write( "\r\n" );
document.write( "    8*sin(6x) + 8*sin(2x) = 0     (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "is equivalent to this one\r\n" );
document.write( "\r\n" );
document.write( "    sin(6x) + sin(2x) = 0         (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(after canceling the factor 8).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In the plot below I show the left side function of equation (2) on the interval [0,2pi).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                 Plot  y = sin(6x) + sin(2x)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the plot, you see that there are 8 roots (solutions) on the interval [0,2pi).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To find all these solutions, you need to solve these equations\r\n" );
document.write( "\r\n" );
document.write( "    6x = 2x,          (3)\r\n" );
document.write( "\r\n" );
document.write( "    6x = 2x +      (4)\r\n" );
document.write( "\r\n" );
document.write( "    6x = 2x +     (5)\r\n" );
document.write( "\r\n" );
document.write( "    6x = 2x +     (6)\r\n" );
document.write( "\r\n" );
document.write( "    6x = 2x +     (7)\r\n" );
document.write( "\r\n" );
document.write( "    6x = 2x +     (8)\r\n" );
document.write( "\r\n" );
document.write( "    6x = 2x +     (9)\r\n" );
document.write( "\r\n" );
document.write( "    6x = 2x +     (10)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Equations (3)- (10) give the solutions x such that 6x and 2x differ in :  then sin(6x) and sin(2x) have the opposite signs.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The solution of these equations is ELEMENTARY, and I leave it to you.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When you complete your calculations, COMPARE the found roots with that you see in the plot.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You are guided, explained, directed and instructed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );