document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061183>Question 1061183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the exact value of sin2ø given that cosø=-12/13 and &#960;<ø<3&#960;/2 without determine the value of ø. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #675987 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=675987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29+=+-12%2F13 ALIGN=MIDDLE  ALT=\"cos%28theta%29+=+-12%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use this to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Pythagorean Identity:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29%2B%28cos%28theta%29%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29%2B%28cos%28theta%29%29%5E2+=+1\"   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%5E2%28theta%29%2B%28-12%2F13%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29%2B%28-12%2F13%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12%2F13 ALIGN=MIDDLE  ALT=\"-12%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > (see \"given\" above)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29%2B144%2F169+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29%2B144%2F169+=+1\"   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%5E2%28theta%29%2B144%2F169-144%2F169+=+1-144%2F169 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29%2B144%2F169-144%2F169+=+1-144%2F169\"   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%5E2%28theta%29+=+1-144%2F169 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29+=+1-144%2F169\"   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%5E2%28theta%29+=+169%2F169-144%2F169 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29+=+169%2F169-144%2F169\"   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%5E2%28theta%29+=+%28169-144%29%2F169 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29+=+%28169-144%29%2F169\"   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%5E2%28theta%29+=+25%2F169 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29+=+25%2F169\"   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=sqrt%28sin%5E2%28theta%29%29+=+sqrt%2825%2F169%29 ALIGN=MIDDLE  ALT=\"sqrt%28sin%5E2%28theta%29%29+=+sqrt%2825%2F169%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%28theta%29+=+-sqrt%2825%2F169%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29+=+-sqrt%2825%2F169%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > See note below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+=+-5%2F13 ALIGN=MIDDLE  ALT=\"sin%28theta%29+=+-5%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > is between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3pi%2F2 ALIGN=MIDDLE  ALT=\"3pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in quadrant 3. This is where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative. So the \"plus/minus\" usually associated with the square root is dropped in favor of just a minus.  \r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "We now have enough to compute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282theta%29 ALIGN=MIDDLE  ALT=\"sin%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the double angle identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282theta%29=2%2Asin%28theta%29%2Acos%28theta%29 ALIGN=MIDDLE  ALT=\"sin%282theta%29=2%2Asin%28theta%29%2Acos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using that identity, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282theta%29=2%2Asin%28theta%29%2Acos%28theta%29 ALIGN=MIDDLE  ALT=\"sin%282theta%29=2%2Asin%28theta%29%2Acos%28theta%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%282theta%29=2%2A%28-5%2F13%29%2A%28-12%2F13%29 ALIGN=MIDDLE  ALT=\"sin%282theta%29=2%2A%28-5%2F13%29%2A%28-12%2F13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the known info\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282theta%29=%282%2A%28-5%29%2A%28-12%29%29%2F%2813%2A13%29 ALIGN=MIDDLE  ALT=\"sin%282theta%29=%282%2A%28-5%29%2A%28-12%29%29%2F%2813%2A13%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%282theta%29=120%2F169 ALIGN=MIDDLE  ALT=\"sin%282theta%29=120%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "The final answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282theta%29=120%2F169 ALIGN=MIDDLE  ALT=\"sin%282theta%29=120%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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