document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204627>Question 1204627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <BR>\n" );
document.write( "sin(x) = − <BR>\n" );
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document.write( " and x is in quadrant III, with 0° ≤ x < 360°, find the exact values of the expressions without solving for x.<BR>\n" );
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document.write( "sin\r<BR>\n" );
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document.write( "x<BR>\n" );
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document.write( "(b)    <BR>\n" );
document.write( "cos\r<BR>\n" );
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document.write( "x<BR>\n" );
document.write( "2\r<BR>\n" );
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document.write( "(c)    <BR>\n" );
document.write( "tan\r<BR>\n" );
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document.write( "x<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 #841003 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=841003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29+=+-20%2F29 ALIGN=MIDDLE  ALT=\"sin%28x%29+=+-20%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is in quadrant III, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+x+%3C+360 ALIGN=MIDDLE  ALT=\"0+%3C=+x+%3C+360\"   DISABLED_style= \"max-width:90%; height:auto;\" >°, find the exact values of the expressions without solving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "in Q III both sin and cos are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negative ALIGN=MIDDLE  ALT=\"negative\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we also know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28x%29%2B+cos%5E2%28x%29=1 ALIGN=MIDDLE  ALT=\"sin%5E2%28x%29%2B+cos%5E2%28x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%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%29=sqrt%281-sin%5E2%28x%29%29 ALIGN=MIDDLE  ALT=\"cos%28x%29=sqrt%281-sin%5E2%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute given value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%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%29=sqrt%281-%28-20%2F29%29%5E2%29 ALIGN=MIDDLE  ALT=\"cos%28x%29=sqrt%281-%28-20%2F29%29%5E2%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%29=sqrt%281-400%2F841%29 ALIGN=MIDDLE  ALT=\"cos%28x%29=sqrt%281-400%2F841%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%29=sqrt%28441%2F841%29 ALIGN=MIDDLE  ALT=\"cos%28x%29=sqrt%28441%2F841%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%29=21%2F29 ALIGN=MIDDLE  ALT=\"cos%28x%29=21%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=-21%2F29 ALIGN=MIDDLE  ALT=\"cos%28x%29=-21%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=-21%2F29 ALIGN=MIDDLE  ALT=\"cos%28x%29=-21%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(a) use Half-Angle Identities\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%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29=sqrt%28%281-cos%28x%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "​<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29=sqrt%28%281-%28-21%2F29%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29=sqrt%28%281-%28-21%2F29%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=sin%28x%2F2%29=sqrt%28%2850%2F29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29=sqrt%28%2850%2F29%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=sin%28x%2F2%29=sqrt%2825%2F29%29 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29=sqrt%2825%2F29%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=%285sqrt%2829%29%29%2F29 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29=%285sqrt%2829%29%29%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29=-%285sqrt%2829%29%29%2F29 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29=-%285sqrt%2829%29%29%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "in Q III\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=-%285sqrt%2829%29%29%2F29 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29=-%285sqrt%2829%29%29%2F29\"   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=sqrt%28%281%2Bcos%28x%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28x%2F2%29=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=cos%28x%2F2%29=sqrt%28%281%2B%28-21%2F29%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28x%2F2%29=sqrt%28%281%2B%28-21%2F29%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=cos%28x%2F2%29=sqrt%284%2F29%29 ALIGN=MIDDLE  ALT=\"cos%28x%2F2%29=sqrt%284%2F29%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=%282sqrt%2829%29%29%2F29 ALIGN=MIDDLE  ALT=\"cos%28x%2F2%29=%282sqrt%2829%29%29%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2F2%29=-%282sqrt%2829%29%29%2F29 ALIGN=MIDDLE  ALT=\"cos%28x%2F2%29=-%282sqrt%2829%29%29%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "in Q III\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=-%282sqrt%2829%29%29%2F29 ALIGN=MIDDLE  ALT=\"cos%28x%2F2%29=-%282sqrt%2829%29%29%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=%281-cos%28x%29%29%2F%281%2Bcos%28x%29%29 ALIGN=MIDDLE  ALT=\"tan%28x%2F2%29=%281-cos%28x%29%29%2F%281%2Bcos%28x%29%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=sqrt%28%281-%28-21%2F29%29%29%2F%281%2B%28-21%2F29%29%29%29 ALIGN=MIDDLE  ALT=\"tan%28x%2F2%29=sqrt%28%281-%28-21%2F29%29%29%2F%281%2B%28-21%2F29%29%29%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=sqrt%2825%2F4%29 ALIGN=MIDDLE  ALT=\"tan%28x%2F2%29=sqrt%2825%2F4%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=5%2F2 ALIGN=MIDDLE  ALT=\"tan%28x%2F2%29=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%2F2%29=-5%2F2 ALIGN=MIDDLE  ALT=\"tan%28x%2F2%29=-5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "In the third quadrant, the values for tan are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=positive ALIGN=MIDDLE  ALT=\"positive\"   DISABLED_style= \"max-width:90%; height:auto;\" > only.\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=+5%2F2 ALIGN=MIDDLE  ALT=\"tan%28x%2F2%29=+5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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