document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161413>Question 1161413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If cos x= -15/17 with x in quadrant III, find the exact value of sin 2x and the quadrant of 2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784971 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=784971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28x%29=+-15%2F17+ ALIGN=MIDDLE  ALT=\"cos+%28x%29=+-15%2F17+\"   DISABLED_style= \"max-width:90%; height:auto;\" >with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >in quadrant III, find the exact value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%282x%29 ALIGN=MIDDLE  ALT=\"sin+%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the quadrant of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28x%29=+-15%2F17+ ALIGN=MIDDLE  ALT=\"cos+%28x%29=+-15%2F17+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%282x%29 ALIGN=MIDDLE  ALT=\"sin+%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "use identity:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29=2sin%28x%29cos%28x%29 ALIGN=MIDDLE  ALT=\"sin%282x%29=2sin%28x%29cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......substitute cos\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282x%29=2sin%28x%29%28-15%2F17%29+ ALIGN=MIDDLE  ALT=\"sin%282x%29=2sin%28x%29%28-15%2F17%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " use  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29=sqrt%281-cos%5E2%28x%29%29 ALIGN=MIDDLE  ALT=\"sin%28x%29=sqrt%281-cos%5E2%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find sin\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%281-%28-15%2F17%29+%5E2%29 ALIGN=MIDDLE  ALT=\"sin%28x%29=sqrt%281-%28-15%2F17%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=sin%28x%29=sqrt%281-225%2F289%29 ALIGN=MIDDLE  ALT=\"sin%28x%29=sqrt%281-225%2F289%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%28%28289-225%29%2F289%29 ALIGN=MIDDLE  ALT=\"sin%28x%29=sqrt%28%28289-225%29%2F289%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%2864%2F289%29 ALIGN=MIDDLE  ALT=\"sin%28x%29=sqrt%2864%2F289%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 ALIGN=MIDDLE  ALT=\"sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F17%29 ALIGN=MIDDLE  ALT=\"8%2F17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In Quadrant III, sine and cosine are negative:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29=-8%2F17 ALIGN=MIDDLE  ALT=\"sin%28x%29=-8%2F17\"   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%282x%29=2%28-8%2F17%29%28-15%2F17%29+ ALIGN=MIDDLE  ALT=\"sin%282x%29=2%28-8%2F17%29%28-15%2F17%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%282x%29=240%2F289 ALIGN=MIDDLE  ALT=\"sin%282x%29=240%2F289\"   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=2x=sin%5E-1%28240%2F289%29 ALIGN=MIDDLE  ALT=\"2x=sin%5E-1%28240%2F289%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=2x=56.14 ALIGN=MIDDLE  ALT=\"2x=56.14\"   DISABLED_style= \"max-width:90%; height:auto;\" >° -> In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I ALIGN=MIDDLE  ALT=\"I\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );