document.write( "Question 1127695: What are the solutions for sin(4x)+sin(x)=0, between the intervals 0 and pi
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Algebra.Com's Answer #744196 by ikleyn(52847) $\"\"$ $\"About$

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document.write( "sin(4x) + sin(x) = 0.      (1)\r\n" );
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document.write( "Use the formula (one of the basic Trigonometry formula)\r\n" );
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document.write( "   sin(a) + sin(b) = ,\r\n" );
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document.write( "which is valid for any angles \"a\" and \"b\".\r\n" );
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document.write( "By applying it, you get from (1)\r\n" );
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document.write( "     = 0.\r\n" );
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document.write( "Thus you must consider two separate cases.\r\n" );
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document.write( "a)  sin(2.5x) = 0  ====>  2.5x = 0,  ,  ,  ,  ,    ====>  x = 0,  ,  ,  ,  ,   =  = same as 0,\r\n" );
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document.write( "                          and after that the roots repeat cyclically.\r\n" );
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document.write( "                          This row of solutions is the same as  0,  ,  ,  ,    and  =  = same as 0.\r\n" );
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document.write( "                          In more compact form, this family of solutions is  ,  k = 0, 1, 2, 3, 4.\r\n" );
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document.write( "b)  sin(1.5x) = 0  ====>  1.5x = 0,  ,  ,    ====>  x = 0,  ,  ,   =  = same as 0,\r\n" );
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document.write( "                          and after that the roots repeat cyclically.\r\n" );
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document.write( "                          This row of solutions is the same as  0,  ,  ,  =  = 0.\r\n" );
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document.write( "                          In more compact form, this family of solutions is  ,  k = 0, 2, 4.\r\n" );
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document.write( "Answer.  There are two families of solutions:\r\n" );
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document.write( "         a)  ,  k = 0, 1, 2, 3, 4  and  b)  ,  k = 0, 2, 4.\r\n" );
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