document.write( "Question 1202414: 3 sinx - 7= 5 sinx -6 when 0 is less than or equal to x is less than or equal to 360. I need help finding the degrees, just the steps to get there. \n" ); document.write( "

Algebra.Com's Answer #837241 by ikleyn(52873) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Your starting equation is THIS\r\n" );
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document.write( "    3*sin(x) - 7 = 5*sin(x) - 6,    0° <= x < 360°.\r\n" );
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document.write( "Simplify it in standard way\r\n" );
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document.write( "    -7 + 6 = 5*sin(x) - 3*sin(x)  (you collect constant terms in the left side;\r\n" );
document.write( "                                   you collect sin-terms in the right side).\r\n" );
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document.write( "You get\r\n" );
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document.write( "      -1  = 2*sin(x).\r\n" );
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document.write( "It implies\r\n" );
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document.write( "       sin(x) = -1/2.    (*)\r\n" );
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document.write( "It is a standard equation to determine \"x\" from the table \r\n" );
document.write( "or from a standard \"unit circle\".\r\n" );
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document.write( "      x = 210° in QIII  (in third quadrant);\r\n" );
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document.write( "      x = 330° in QIV  (in fourth quadrant).\r\n" );
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document.write( "    +------------------------------------------------------------------+\r\n" );
document.write( "    |  From equation (*), you should get these solutions momentarily   |\r\n" );
document.write( "    |  from your head: you MUST KNOW IT as the multiplication table.   |\r\n" );
document.write( "    +------------------------------------------------------------------+\r\n" );
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document.write( "The problem is just solved.\r\n" );
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document.write( "Your original equation has two roots in the given interval.\r\n" );
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document.write( "The solutions are  x = 210° in QIII  and  x = 330° in QIV.\r\n" );
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\n" ); document.write( "\n" ); document.write( "You get full explanation from me and complete mantra
\n" ); document.write( "to pronounce it when solving such equations.\r
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me for my teaching.\r
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