document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204118>Question 1204118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If tan(x) = −40/9 and x is in quadrant IV, with 0° ≤ x < 360°, find the exact values of the expressions without solving for x.<BR>\n" );
document.write( "(a)  sin(x/2)\r<BR>\n" );
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document.write( "(b)  cos(x/2)\r<BR>\n" );
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document.write( "(c)  tan(x/2)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840166 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=840166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29+=+-40%2F9 ALIGN=MIDDLE  ALT=\"tan%28x%29+=+-40%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=tan%28x%29+=+sin%28x%29%2Fcos%28x%29 ALIGN=MIDDLE  ALT=\"tan%28x%29+=+sin%28x%29%2Fcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "also, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29+=+opp%2Fadj ALIGN=MIDDLE  ALT=\"tan%28x%29+=+opp%2Fadj\"   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=+opp+%2F+hyp+ ALIGN=MIDDLE  ALT=\"sin+%28x%29=+opp+%2F+hyp+\"   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%29+=+adj+%2F+hyp ALIGN=MIDDLE  ALT=\"cos+%28x%29+=+adj+%2F+hyp\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=opp%2Fadj=+-40%2F9+ ALIGN=MIDDLE  ALT=\"opp%2Fadj=+-40%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=opp=-40 ALIGN=MIDDLE  ALT=\"opp=-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=adj=9 ALIGN=MIDDLE  ALT=\"adj=9\"   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=hyp=sqrt%28%28-40%29%5E2%2B9%5E2%29=41 ALIGN=MIDDLE  ALT=\"hyp=sqrt%28%28-40%29%5E2%2B9%5E2%29=41\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28x%29=+-40%2F+41 ALIGN=MIDDLE  ALT=\"sin+%28x%29=+-40%2F+41\"   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%29+=+9+%2F+41+ ALIGN=MIDDLE  ALT=\"cos+%28x%29+=+9+%2F+41+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(a)\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;\" >\r<BR>\n" );
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document.write( "using Half Angle Formulas\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+=sqrt+%28+%281+-+cos%28x%29%29+%2F+2+%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29+=sqrt+%28+%281+-+cos%28x%29%29+%2F+2+%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%2F2%29+=+%28+%281+-%289+%2F+41%29%29+%2F+2+%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29+=+%28+%281+-%289+%2F+41%29%29+%2F+2+%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%2F2%29+=+sqrt+%28+16%2F41+%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29+=+sqrt+%28+16%2F41+%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%2F2%29+=++4%2Fsqrt+%28+41+%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29+=++4%2Fsqrt+%28+41+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28x%2F2%29+=++-+4%2Fsqrt+%28+41+%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29+=++-+4%2Fsqrt+%28+41+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "sin is negative in Q IV\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+=+-+4%2Fsqrt+%28+41+%29 ALIGN=MIDDLE  ALT=\"sin+%28x%2F2%29+=+-+4%2Fsqrt+%28+41+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b)\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;\" >\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+%2B+%289+%2F+41%29%29+%2F+2+%29 ALIGN=MIDDLE  ALT=\"cos+%28x%2F2%29+=+sqrt+%28+%281+%2B+%289+%2F+41%29%29+%2F+2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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+%2850%2F41%29+%2F+2+%29+ ALIGN=MIDDLE  ALT=\"cos+%28x%2F2%29+=+sqrt+%28+%2850%2F41%29+%2F+2+%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+=+sqrt+%28+25%2F41+%29+ ALIGN=MIDDLE  ALT=\"cos+%28x%2F2%29+=+sqrt+%28+25%2F41+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28x%2F2%29+=+5%2Fsqrt%2841%29 ALIGN=MIDDLE  ALT=\"cos+%28x%2F2%29+=+5%2Fsqrt%2841%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...cos is positive in Q IV\r<BR>\n" );
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document.write( "(c)\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=-%284%2Fsqrt+%28+41+%29%29%2F%285%2F+sqrt%2841%29%29=-4%2F5 ALIGN=MIDDLE  ALT=\"tan%28x%2F2%29=-%284%2Fsqrt+%28+41+%29%29%2F%285%2F+sqrt%2841%29%29=-4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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