document.write( "Question 973516: Please help!!!! State all the solutions to sin(x) + 2 sin(2x)= √(x). \n" ); document.write( "
Algebra.Com's Answer #595674 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
sin(x) + 2 sin(2x)= √(x).
\n" ); document.write( "
\r\n" );
document.write( "There are no standard algebraic or trigonometric methods for solving an \r\n" );
document.write( "equation like this one which contains a variable which is both \r\n" );
document.write( "\r\n" );
document.write( "1. part of a trigonometric function, as in the term sin(x)\r\n" );
document.write( "\r\n" );
document.write( "and also\r\n" );
document.write( "\r\n" );
document.write( "2. not part of a trigonometric function, as in the term √(x).\r\n" );
document.write( "\r\n" );
document.write( "They can be solved by iterative (guess and check) methods. That's the method of\r\n" );
document.write( "computers and graphing calculators.  At lightning speed they guess an\r\n" );
document.write( "approximate solution and then successively improve on it, getting closer and\r\n" );
document.write( "closer, and eventually getting as close as is desired to the actual solution.\r\n" );
document.write( " \r\n" );
document.write( "Occasionally a solution will be obvious.  Such is the case in this one, as an\r\n" );
document.write( "obvious solution is x = 0.\r\n" );
document.write( "\r\n" );
document.write( "In addition to the x = 0 solution, there are four other solutions.  I have\r\n" );
document.write( "approximated them by a computer program below:\r\n" );
document.write( "\r\n" );
document.write( "x ~ 0.0400728749475875660160835459576477048399766237746285782270624983...\r\n" );
document.write( "\r\n" );
document.write( "x ~ 1.51275945812645026464843139037785711835717362190264861068799171...\r\n" );
document.write( "\r\n" );
document.write( "x ~ 7.00697814299500935029704040024283479348882650864271753095319661...\r\n" );
document.write( "\r\n" );
document.write( "x ~ 7.25027785575978077317786523805533381477772319549846961135371664...\r\n" );
document.write( "\r\n" );
document.write( "where ~ means \"is approximately equal to\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );