document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=756874>Question 756874</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I Solve the trigonometric equation for<BR>\n" );
document.write( "1)tan3x=1               \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #460460 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=460460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One solution for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%283x%29=1 ALIGN=MIDDLE  ALT=\"tan%283x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > comes from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=45%5Eo ALIGN=MIDDLE  ALT=\"3x=45%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=pi%2F4 ALIGN=MIDDLE  ALT=\"3x=pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The period of the function tangent is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can express all solutions, using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >= any integer, as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=45%5Eo%2Bk%2A180%5Eo ALIGN=MIDDLE  ALT=\"3x=45%5Eo%2Bk%2A180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2845%5Eo%2Bk%2A180%5Eo%29%2F3 ALIGN=MIDDLE  ALT=\"x=%2845%5Eo%2Bk%2A180%5Eo%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=15%5Eo%2Bk%2A60%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%28x=15%5Eo%2Bk%2A60%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=pi%2F4%2Bk%2Api ALIGN=MIDDLE  ALT=\"3x=pi%2F4%2Bk%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28%28pi%2F4%2Bk%2Api%29%29%2F3 ALIGN=MIDDLE  ALT=\"x=%28%28pi%2F4%2Bk%2Api%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > -->  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=pi%2F12%2Bk%2Api%2F3 ALIGN=MIDDLE  ALT=\"x=pi%2F12%2Bk%2Api%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=pi%2F12%2B4k%2Api%2F12 ALIGN=MIDDLE  ALT=\"x=pi%2F12%2B4k%2Api%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=%284k%2B1%29pi%2F12%29 ALIGN=MIDDLE  ALT=\"highlight%28x=%284k%2B1%29pi%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "EXTRA:<BR>\n" );
document.write( "If you are looking for solutions between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%5Eo ALIGN=MIDDLE  ALT=\"0%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5EO ALIGN=MIDDLE  ALT=\"360%5EO\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0 ALIGN=MIDDLE  ALT=\"k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=15%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%28x=15%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=1 ALIGN=MIDDLE  ALT=\"k=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B1%2A60%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B1%2A60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B60%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=75%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%28x=75%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=2 ALIGN=MIDDLE  ALT=\"k=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B2%2A60%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B2%2A60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B120%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B120%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=135%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%28x=135%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B3%2A60%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B3%2A60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B180%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=195%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%28x=195%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=4 ALIGN=MIDDLE  ALT=\"k=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B4%2A60%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B4%2A60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B240%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B240%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=255%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%28x=255%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B5%2A60%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B5%2A60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B300%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B300%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=315%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%28x=315%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We stop at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=6 ALIGN=MIDDLE  ALT=\"k=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B6%2A60%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B6%2A60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%5Eo%2B360%5Eo=375%3E360%5Eo ALIGN=MIDDLE  ALT=\"x=15%5Eo%2B360%5Eo=375%3E360%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Measuring angles in radians instead of degrees, the solutions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=x%3C2pi ALIGN=MIDDLE  ALT=\"0%3C=x%3C2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "can be calculated from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284k%2B1%29pi%2F12 ALIGN=MIDDLE  ALT=\"x=%284k%2B1%29pi%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > making <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 0, 1, 2, 3, 4, and 5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0 ALIGN=MIDDLE  ALT=\"k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=pi%2F12%29 ALIGN=MIDDLE  ALT=\"highlight%28x=pi%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=1 ALIGN=MIDDLE  ALT=\"k=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2A1%2B1%29pi%2F12 ALIGN=MIDDLE  ALT=\"x=%284%2A1%2B1%29pi%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%285pi%2F12%29 ALIGN=MIDDLE  ALT=\"highlight%285pi%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=2 ALIGN=MIDDLE  ALT=\"k=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2A2%2B1%29pi%2F12 ALIGN=MIDDLE  ALT=\"x=%284%2A2%2B1%29pi%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289pi%2F12%29 ALIGN=MIDDLE  ALT=\"highlight%289pi%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2A3%2B1%29pi%2F12 ALIGN=MIDDLE  ALT=\"x=%284%2A3%2B1%29pi%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2813pi%2F12%29 ALIGN=MIDDLE  ALT=\"highlight%2813pi%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=4 ALIGN=MIDDLE  ALT=\"k=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2A4%2B1%29pi%2F12 ALIGN=MIDDLE  ALT=\"x=%284%2A4%2B1%29pi%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2817pi%2F12%29 ALIGN=MIDDLE  ALT=\"highlight%2817pi%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2A5%2B1%29pi%2F12 ALIGN=MIDDLE  ALT=\"x=%284%2A5%2B1%29pi%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2821pi%2F12%29 ALIGN=MIDDLE  ALT=\"highlight%2821pi%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );