document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131784>Question 1131784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find sin x/2, cos x/2, and tan x/2from the given information. sec x = 9/8,   270° < x < 360° </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748471 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28x%2F2%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+x%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28+x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+tan+%28x%2F2%29 ALIGN=MIDDLE  ALT=\"+tan+%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the given information:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec+%28x+%29=+9%2F8 ALIGN=MIDDLE  ALT=\"sec+%28x+%29=+9%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270 ALIGN=MIDDLE  ALT=\"270\"   DISABLED_style= \"max-width:90%; height:auto;\" >° < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > < <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360 ALIGN=MIDDLE  ALT=\"360\"   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=sec+%28x+%29=+9%2F8=hypotenuse%2Fadjacent_side ALIGN=MIDDLE  ALT=\"sec+%28x+%29=+9%2F8=hypotenuse%2Fadjacent_side\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hypotenuse=9 ALIGN=MIDDLE  ALT=\"hypotenuse=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=adjacent_+side=8 ALIGN=MIDDLE  ALT=\"adjacent_+side=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=opposite_side=sqrt%289%5E2-8%5E2%29=sqrt%2881-64%29=sqrt%2817%29 ALIGN=MIDDLE  ALT=\"opposite_side=sqrt%289%5E2-8%5E2%29=sqrt%2881-64%29=sqrt%2817%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=sin+%28x%29=-sqrt%2817%29%2F9 ALIGN=MIDDLE  ALT=\"sin+%28x%29=-sqrt%2817%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in quadrant IV where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29+%3C+0 ALIGN=MIDDLE  ALT=\"sin%28x%29+%3C+0\"   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=cos%28+x%29=8%2F9 ALIGN=MIDDLE  ALT=\"cos%28+x%29=8%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Identities you need to use:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28x%2F2%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281-cos+%28x%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%281-cos+%28x%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "choose positive root because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F2%29 ALIGN=MIDDLE  ALT=\"%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in quadrant II where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28x%29+%3E+0 ALIGN=MIDDLE  ALT=\"+sin%28x%29+%3E+0\"   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=sin+%28x%2F2%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281-cos+x%29%2F2%29=sqrt%28%281-8%2F9%29%2F2%29=sqrt%281%2F18%29 ALIGN=MIDDLE  ALT=\"sqrt%28%281-cos+x%29%2F2%29=sqrt%28%281-8%2F9%29%2F2%29=sqrt%281%2F18%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=cos+%28x%2F2%29 ALIGN=MIDDLE  ALT=\"cos+%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2Bcos%28+x%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%281%2Bcos%28+x%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "choose negative root because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F2%29 ALIGN=MIDDLE  ALT=\"%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in quadrant II where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29%3C+0 ALIGN=MIDDLE  ALT=\"cos%28x%29%3C+0\"   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=cos+%28x%2F2%29=-sqrt%28%281%2Bcos+%28x%29%29%2F2%29=-sqrt%28%281%2B8%2F9%29%2F2%29=-sqrt%2817%2F18%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=tan%28+x%2F2%29=sin%28x%29%2F%281%2Bcos+%28x%29%29=-sqrt%2817%29%2F9%2F%281%2B8%2F9%29=-sqrt%2817%29%2F17 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "How to check answers with calculator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec+%28x%29=9%2F8 ALIGN=MIDDLE  ALT=\"sec+%28x%29=9%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28x%29=8%2F9 ALIGN=MIDDLE  ALT=\"cos+%28x%29=8%2F9\"   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=cos%5E-1%288%2F9%29 ALIGN=MIDDLE  ALT=\"cos%5E-1%288%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >&#8776; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.47588225 ALIGN=MIDDLE  ALT=\"0.47588225\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians &#8776;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27.27 ALIGN=MIDDLE  ALT=\"27.27\"   DISABLED_style= \"max-width:90%; height:auto;\" >° (reference angle in specified quadrant IV)\r<BR>\n" );
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document.write( "standard position of angle=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360-27.27%B0=332.73 ALIGN=MIDDLE  ALT=\"360-27.27%B0=332.73\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2=332.73%2F2=166.37 ALIGN=MIDDLE  ALT=\"x%2F2=332.73%2F2=166.37\"   DISABLED_style= \"max-width:90%; height:auto;\" >º\r<BR>\n" );
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document.write( "reference angle=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180-166.37=13.63 ALIGN=MIDDLE  ALT=\"180-166.37=13.63\"   DISABLED_style= \"max-width:90%; height:auto;\" >º\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28x%2F2%29=sin+%2813.63%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29=sin+%2813.63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8776;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2357 ALIGN=MIDDLE  ALT=\"0.2357\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......(in quadrant II where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29+%3E+0 ALIGN=MIDDLE  ALT=\"sin%28x%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "and above we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28x%2F2%29=sqrt%281%2F18%29=0.2357 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29=sqrt%281%2F18%29=0.2357\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....which confirms our solution\r<BR>\n" );
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document.write( "you can check <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28x%2F2%29 ALIGN=MIDDLE  ALT=\"cos+%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and tan <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F2%29 ALIGN=MIDDLE  ALT=\"%28x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the same way \r<BR>\n" );
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document.write( " </SPAN>\n" );
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