document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031958>Question 1031958</A>: <I><SPAN STYLE=\"word-break: break-all;\"> He all, Can somebody explain me the reason why for this equation:\r<BR>\n" );
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document.write( "tan(10° - 4x) = -1/3^(1/2)\r<BR>\n" );
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document.write( "the proposed solution is x=10°-k45° and not x=10°-k180°\r<BR>\n" );
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document.write( "This brings to the following 8 results in the first round of 360°:<BR>\n" );
document.write( "10°, 55°, 100°, 145°, 190°, 235°, 280°, 325°<BR>\n" );
document.write( "What causes this coeff k45° to be applied?<BR>\n" );
document.write( "Thank you very much and regards </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646631 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52879)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=646631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "He all, Can somebody explain me the reason why for this equation:\r<BR>\n" );
document.write( "\n" );
document.write( "tan(10° - 4x) = -1/sqrt(3)\r<BR>\n" );
document.write( "\n" );
document.write( "the proposed solution is x=10°-k45° and not x=10°-k180°\r<BR>\n" );
document.write( "\n" );
document.write( "This brings to the following 8 results in the first round of 360°:<BR>\n" );
document.write( "10°, 55°, 100°, 145°, 190°, 235°, 280°, 325°<BR>\n" );
document.write( "What causes this coeff k45° to be applied?<BR>\n" );
document.write( "Thank you very much and regards<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "tan(10° - 4x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"-1%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   --->\r\n" );
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document.write( "10° - 4x = -30° + k*180°         (I wrote \" + k*180° \", since 180° is the period of the tangent function).\r\n" );
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document.write( "From this equation we have \r\n" );
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document.write( "4x = 40°  - k*180°,  k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "and hence\r\n" );
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document.write( "x = 10° - k*45°,  k = 0, +/-1, +/-2, . . . \r\n" );
document.write( "</PRE><BR>\n" );
document.write( " </SPAN>\n" );
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