document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155366>Question 1155366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to answer this:\r<BR>\n" );
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document.write( "For 0° ≤  x  ≤  360°, find the number of roots the equation 2sinxtanx = -tanx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777944 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=777944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first thing is to look for zeros:<BR>\n" );
document.write( "tan(x)=0 at  0, 180, and 360 degrees, and these are all solutions.<BR>\n" );
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document.write( "For non-zero solutions:\r<BR>\n" );
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document.write( "Simplify  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%28x%29tan%28x%29+=+-tan%28x%29+ ALIGN=MIDDLE  ALT=\"2sin%28x%29tan%28x%29+=+-tan%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28x%29+=+-1%2F2+ ALIGN=MIDDLE  ALT=\"+sin%28x%29+=+-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29%3C%3E0 ALIGN=MIDDLE  ALT=\"tan%28x%29%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and recall:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2830%5Eo%29+=+1%2F2+ ALIGN=MIDDLE  ALT=\"sin%2830%5Eo%29+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "in Q1,Q2,Q3,Q4, sin(x) is +,+,-,-, respectively.<br>\r<BR>\n" );
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document.write( "Working from the x-axis, push the angle into Q3 by adding 180+30 = 210 and into Q4 by subtracting 30 from 360, giving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28310%29 ALIGN=MIDDLE  ALT=\"cross%28310%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >330  (edited typo here).<br>\r<BR>\n" );
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document.write( "Solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28matrix%281%2C9%2C0%5Eo%2C%22%2C%22%2C180%5Eo%2C%22%2C%22%2C210%5Eo%2C%22%2C%22%2C330%5Eo%2C%22%2Cand%22+%2C360%5Eo%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A picture is worth a thousand words:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_helper&illustration_name=sin_tan\">\r<BR>\n" );
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document.write( "And note if you rearrange to 2sin(x)tan(x)+tan(x) = 0  and graph the LHS, you can simply look for where this rearranged function crosses the x-axis:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_helper&illustration_name=sin_tan_p_tan_eq0\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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