document.write( "Question 1045455: Please help. I would like the answer in radians. Thanks!
\n" ); document.write( "2cos^2x + sinx -1 =0 \n" ); document.write( "

Algebra.Com's Answer #660909 by ikleyn(52847) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Please help. I would like the answer in radians. Thanks!
\n" ); document.write( "2cos^2x + sinx -1 =0
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "First what we need to do is to reduce the given equation to the quadratic equation for sin(x).\r\n" );
document.write( "For it, use the identity cos^2(x) = 1-sin^2(x) and replace cos^2(x) in the equation by this expression. You will get\r\n" );
document.write( "\r\n" );
document.write( "2*(1-sin^2(x) + sin(x) - 1 = 0,   or\r\n" );
document.write( "\r\n" );
document.write( "2 - 2sin^2(x) + sin(x) - 1 = 0,   or\r\n" );
document.write( "\r\n" );
document.write( "2sin^2(x) - sin(x) - 1 = 0.\r\n" );
document.write( "\r\n" );
document.write( "Factor left side:\r\n" );
document.write( "\r\n" );
document.write( "(2sin(x) + 1)*(sin(x) - 1) = 0.\r\n" );
document.write( "\r\n" );
document.write( "Now the equation deploys in two independent equations:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1.  2sin(x) + 1 = 0  --->  sin(x) =   --->  x =   and/or  x = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  sin(x) - 1 = 0  --->  sin(x) = 1  --->  x = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The solutions are  x = ,   and  .\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( " \r\n" ); document.write( " \r\n" ); document.write( " \r\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Plot y = $\"2cos%5E2%28x%29+%2B+sin%28x%29+-1\"$ \r
\n" ); document.write( "\n" ); document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );