document.write( "Question 958870: Find all solutions of the following equation: tan (theta/8) +sqrt3 = 0. find the solutions in the interval [0, 2pi]
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Algebra.Com's Answer #854574 by ikleyn(53937) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "        In his post, @lwsshar3 gives the answer   x = 16π/3, 40π/3.\r
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\n" ); document.write( "\n" ); document.write( "        This answer is INCORRECT, since both these values are OUT of the interval [0,2pi).\r
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\n" ); document.write( "\n" ); document.write( "        See below my correct solution.\r
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document.write( "tan(x/8) + √3 = 0,    (1)\r\n" );
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document.write( "tan(x/8) = -√3.       (2)\r\n" );
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document.write( "We are looking for possible solutions 'x' in interval [,). \r\n" );
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document.write( "So, x/8 should be in interval [0,), which is the same as interval [0,). \r\n" );
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document.write( "But in this interval from 0 to , function tan is always non-negative.\r\n" );
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document.write( "Hence, equation (2) with the negative right side HAS NO solutions in this interval.\r\n" );
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document.write( "It implies that the original equation has no solution/solutions in the given interval [0,2pi).     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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\n" ); document.write( "\n" ); document.write( "Ignore the post by @lwsshar3, since it is totally wrong.\r
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