document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204691>Question 1204691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if csc x=3, 90 degrees< x < 180 degrees\r<BR>\n" );
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document.write( "then,\r<BR>\n" );
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document.write( "sin (x/2)<BR>\n" );
document.write( "cos (x/2)<BR>\n" );
document.write( "tan (x/2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841119 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=841119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Hint #1<BR>\n" );
document.write( "When 90 < x < 180, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28x%29+=+3 ALIGN=MIDDLE  ALT=\"csc%28x%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > leads to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29+=+-2%2Asqrt%282%29%2F3 ALIGN=MIDDLE  ALT=\"cos%28x%29+=+-2%2Asqrt%282%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hint #2<BR>\n" );
document.write( "90 < x < 180 has all sides cut in half to 45 < x/2 < 90<BR>\n" );
document.write( "Angle x/2 is in quadrant 1 where all 6 trig functions are positive\r<BR>\n" );
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document.write( "Hint #3<BR>\n" );
document.write( "The half angle identities are<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2F2%29+=+%22%22%2B-sqrt%28+%281%2Bcos%28x%29%29%2F2+%29 ALIGN=MIDDLE  ALT=\"cos%28x%2F2%29+=+%22%22%2B-sqrt%28+%281%2Bcos%28x%29%29%2F2+%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=tan%28x%2F2%29+=+%22%22%2B-sqrt%28+%281-cos%28x%29%29%2F%281%2Bcos%28x%29%29+%29 ALIGN=MIDDLE  ALT=\"tan%28x%2F2%29+=+%22%22%2B-sqrt%28+%281-cos%28x%29%29%2F%281%2Bcos%28x%29%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, keep the 2nd hint in mind, so we can drop the plus minus to write<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C3%2Ccos%28x%2F2%29+=+sqrt%28+%281%2Bcos%28x%29%29%2F2+%29%2C+%22+when+%22%2C+45+%3C+x%2F2+%3C+90%29 ALIGN=MIDDLE   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%2C3%2Ctan%28x%2F2%29+=+sqrt%28+%281-cos%28x%29%29%2F%281%2Bcos%28x%29%29+%29%2C+%22+when+%22%2C+45+%3C+x%2F2+%3C+90%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Or once you know what sin(x/2) and cos(x/2) are, you can compute tangent like so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%2F2%29+=+%28sin%28x%2F2%29%29%2F%28cos%28x%2F2%29%29 ALIGN=MIDDLE  ALT=\"tan%28x%2F2%29+=+%28sin%28x%2F2%29%29%2F%28cos%28x%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "More trig identities can be found here<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf\">https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf</a><BR>\n" );
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