document.write( "Question 119090: how do i solve the following equation for values of x in the range
\n" ); document.write( "0 degrees < x <360 degrees\r
\n" ); document.write( "\n" ); document.write( "6sin^2 x - sinx - 2 = 0 \n" ); document.write( "
Algebra.Com's Answer #87227 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
how do i solve the following equation for values of x in the range
\n" ); document.write( "0° < x < 360°
\n" ); document.write( "
\r\n" );
document.write( "6sin²x - sinx - 2 = 0\r\n" );
document.write( "\r\n" );
document.write( "Let w = sinx\r\n" );
document.write( "\r\n" );
document.write( "Then w² = sin²x\r\n" );
document.write( "\r\n" );
document.write( "6w² - w - 2 = 0\r\n" );
document.write( "\r\n" );
document.write( "Factor as\r\n" );
document.write( "\r\n" );
document.write( "(2w + 1)(3w - 2) = 0\r\n" );
document.write( "\r\n" );
document.write( "2w + 1 = 0;   3w - 2 = 0\r\n" );
document.write( "    2w = -1;      3w = 2\r\n" );
document.write( "     w = \"-1%2F2\";      w = \"2%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "Now replace w by sinx\r\n" );
document.write( "\r\n" );
document.write( "   sinx = \"-1%2F2\";   sinx = \"2%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "The first one can be solved as special angles.\r\n" );
document.write( "The sine is negative in the 3rd and 4th quadrants,\r\n" );
document.write( "and since the reference angle 30° has sine +\"1%2F2\",\r\n" );
document.write( "the angles in the 3rd and 4th quadrants having that\r\n" );
document.write( "sine are 210° and 330°.\r\n" );
document.write( "\r\n" );
document.write( "The second one can't be solved as a special angles.\r\n" );
document.write( "The sine is positive in the 1st and 2nd quadrants,\r\n" );
document.write( "We find the refrence angle using inverse sine on a\r\n" );
document.write( "calculator as 41.8103149°. So the angles in the 1st\r\n" );
document.write( "and 2nd quadrants having that sine are 41.8103149°\r\n" );
document.write( "for the 1st quadrant answer and to find the 2nd \r\n" );
document.write( "quadrant answer we subtract 41.8103149° from 180°.\r\n" );
document.write( "\r\n" );
document.write( "180° - 41.8103149° = 138.1896861°\r\n" );
document.write( "\r\n" );
document.write( "The four solutions are:\r\n" );
document.write( "\r\n" );
document.write( "x =  210°, 330°, 41.8103149°, and 138.1896861°\r\n" );
document.write( "\r\n" );
document.write( "Edwin\r\n" );
document.write( "
\n" ); document.write( "
\n" );