document.write( "Question 1069081: Give the general solution to the equation sinx+sin2x+sin3x=0 \n" ); document.write( "

Algebra.Com's Answer #684306 by ikleyn(52839) $\"\"$ $\"About$

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\n" ); document.write( "Give the general solution to the equation sinx+sin2x+sin3x=0
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document.write( "sin(x) + sin(2x) + sin(3x) = 0.     (1)\r\n" );
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document.write( "Apply the trigonometry formula   = \r\n" );
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document.write( "     (see any serious textbook in trigonometry or the lessons \r\n" );
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document.write( "         - FORMULAS FOR TRIGONOMETRIC FUNCTIONS\r\n" );
document.write( "         - Addition and subtraction of trigonometric functions\r\n" );
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document.write( "      in this site) to the first and third addend in the left side of the original equation (1).   You will get\r\n" );
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document.write( " =  =  = .\r\n" );
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document.write( "Now, the equation (1) takes the form\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( " = .\r\n" );
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document.write( "This equation deploys in two independent equations\r\n" );
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document.write( "1.  sin(2x) = 0  --->  x = , x = ,  k = 0, =/-1, +/-2. . . . \r\n" );
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document.write( "2.  2cos(x) + 1 = 0  --->  cos(x) =   --->  x = ,  x = ,  k = 0, =/-1, +/-2. . . . \r\n" );
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document.write( "Answer.  The solutions are  a)  x = , x = ,  k = 0, =/-1, +/-2. . . .    and \r\n" );
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document.write( "                            b)  x = ,  x = ,  k = 0, =/-1, +/-2. . . . \r\n" );
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document.write( "Plot y = sin(x) + sin(2x) + sin(3x)\r\n" );
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\n" ); document.write( "\n" ); document.write( "The solution by the other tutor is incorrect.\r
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