document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204852>Question 1204852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the measure of the principal angle that is coterminal with the given angle?<BR>\n" );
document.write( "23π/6\r<BR>\n" );
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document.write( "11π/6 is in the answer key, but I can’t solve it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841389 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Grab a calculator to find that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2823pi%29%2F6+=+12.042772 ALIGN=MIDDLE  ALT=\"%2823pi%29%2F6+=+12.042772\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately<BR>\n" );
document.write( "Recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi+=+6.28 ALIGN=MIDDLE  ALT=\"2pi+=+6.28\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately, so we need to find a coterminal angle between 0 and 6.28 roughly.<BR>\n" );
document.write( "Unfortunately 12.042772 is not between 0 and 6.28\r<BR>\n" );
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document.write( "Subtract off <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > to rotate the angle 360 degrees, and land on a coterminal angle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2823pi%29%2F6-2pi ALIGN=MIDDLE  ALT=\"%2823pi%29%2F6-2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2823pi%29%2F6-2pi%2A%286%2F6%29 ALIGN=MIDDLE  ALT=\"%2823pi%29%2F6-2pi%2A%286%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2823pi%29%2F6-%2812pi%29%2F6 ALIGN=MIDDLE  ALT=\"%2823pi%29%2F6-%2812pi%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2823pi-12pi%29%2F6 ALIGN=MIDDLE  ALT=\"%2823pi-12pi%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811pi%29%2F6 ALIGN=MIDDLE  ALT=\"%2811pi%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As a check, this result should be between 0 and 6.28 radians.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811pi%29%2F6+=+5.759587 ALIGN=MIDDLE  ALT=\"%2811pi%29%2F6+=+5.759587\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately\r<BR>\n" );
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document.write( "Another approach\r<BR>\n" );
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document.write( "This method is a bit longer, but it's something to consider.\r<BR>\n" );
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document.write( "Multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2Fpi ALIGN=MIDDLE  ALT=\"180%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" > to convert from radians to degrees.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2823pi%29%2F6%29%2A%28180%2Fpi%29+=+690 ALIGN=MIDDLE  ALT=\"%28%2823pi%29%2F6%29%2A%28180%2Fpi%29+=+690\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C5%2C%2823pi%29%2F6%2C%22radians%22%2C%22=%22%2C690%2C%22degrees%22%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C5%2C%2823pi%29%2F6%2C%22radians%22%2C%22=%22%2C690%2C%22degrees%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The angle 690 degrees is not between 0 and 360. <BR>\n" );
document.write( "Subtract off 360 (repeatedly) until landing somewhere in this interval.\r<BR>\n" );
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document.write( "690-360 = 330<BR>\n" );
document.write( "We're now between 0 and 360.\r<BR>\n" );
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document.write( "Angles 690 degrees and 330 degrees are coterminal. <BR>\n" );
document.write( "They point in the same direction (somewhere in the southeast quadrant).\r<BR>\n" );
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document.write( "Lastly, we convert from degrees to radians. <BR>\n" );
document.write( "Use the conversion factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F180 ALIGN=MIDDLE  ALT=\"pi%2F180\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the reciprocal of the previous conversion factor used.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=330%2A%28pi%2F180%29+=+%2811pi%29%2F6 ALIGN=MIDDLE  ALT=\"330%2A%28pi%2F180%29+=+%2811pi%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C5%2C330%2C%22degrees%22%2C%22=%22%2C%2811pi%29%2F6%2C%22radians%22%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C5%2C330%2C%22degrees%22%2C%22=%22%2C%2811pi%29%2F6%2C%22radians%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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