document.write( "Question 661718: Solve the equation for all solutions in the interval 0degree ≤ x < 360degree.\r
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Algebra.Com's Answer #411779 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If you understand how to solve this algebraic equation for y:  \r\n" );
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document.write( "                  2y² - y - 1 = 0\r\n" );
document.write( "              (2y + 1)(y - 1) = 0\r\n" );
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document.write( "            2y + 1 =  0;   y - 1 = 0\r\n" );
document.write( "                2y = -1;       y = 1\r\n" );
document.write( "                 y = \"-1%2F2\"  \r\n" );
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document.write( "then you can understand how to solve this trigonometric equation\r\n" );
document.write( "for sin(x):\r\n" );
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document.write( "         2sin²(x) - sin(x) - 1 = 0              \r\n" );
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document.write( "    [2sin(x) + 1][sin(x) - 1] = 0\r\n" );
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document.write( "   2sin(x) + 1 = 0;     sin(x) - 1 = 0\r\n" );
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document.write( "      2sin(x) = -1;         sin(x) = 1\r\n" );
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document.write( "       sin(x) = \"-1%2F2\"\r\n" );
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document.write( "To solve\r\n" );
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document.write( "sin(x) = \"-1%2F2\"\r\n" );
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document.write( "2e remember that sin(30°) = \"1%2F2\" then \r\n" );
document.write( "you know that 30° is the reference angle.  The\r\n" );
document.write( "fact that the sine is a negative number, that\r\n" );
document.write( "tell you that the angle x is in the 3rd or\r\n" );
document.write( "4th quadrant.\r\n" );
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document.write( "To get the angle in the 3rd quadrant which has \r\n" );
document.write( "referent angle 30², we add 30² to 180° and get\r\n" );
document.write( "210°.\r\n" );
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document.write( "To get the angle in the 4th quadrant which has \r\n" );
document.write( "referent angle 30², we subtract 30° from 360° \r\n" );
document.write( "and get 330°.\r\n" );
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document.write( "So two of the solutions are 210° and 330°. \r\n" );
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document.write( "To solve sin(x) = 1,\r\n" );
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document.write( "we remember that sin(90°) = 1\r\n" );
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document.write( "So the other solution is 90°.\r\n" );
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document.write( "The three solutions are then:\r\n" );
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document.write( "x = 90°, x = 210°, and x = 330°\r\n" );
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document.write( "Edwin
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