document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138396>Question 1138396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If theta is a third quadrant angle and cos theta = -2/3, find sin theta. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756201 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=756201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  \r<BR>\n" );
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document.write( "If theta is a third quadrant angle and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+theta%29+=+-2%2F3 ALIGN=MIDDLE  ALT=\"cos%28+theta%29+=+-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 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( "From the sign on the cosine value, I only know that the angle is in QII or QIII. That's why they had to give me that additional specification: so I'd know which of those quadrants I'm in.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+theta%29+=+-2%2F3 ALIGN=MIDDLE  ALT=\"cos%28+theta%29+=+-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fr ALIGN=MIDDLE  ALT=\"x%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The Pythagorean Theorem gives me:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+x%5E2+%2B+y%5E2+ ALIGN=MIDDLE  ALT=\"r%5E2+=+x%5E2+%2B+y%5E2+\"   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=3%5E2+=+%28-2%29%5E2+%2B+y%5E2+ ALIGN=MIDDLE  ALT=\"3%5E2+=+%28-2%29%5E2+%2B+y%5E2+\"   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=9+=+4+%2B+y%5E2+ ALIGN=MIDDLE  ALT=\"9+=+4+%2B+y%5E2+\"   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=9-4+=+y%5E2+ ALIGN=MIDDLE  ALT=\"9-4+=+y%5E2+\"   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=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >=±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since  in QIII,  below the x-axis, so y is negative. <BR>\n" );
document.write( "I'll take the negative solution to the equation, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-sqrt%285%29 ALIGN=MIDDLE  ALT=\"y=+-sqrt%285%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=y%2Fr ALIGN=MIDDLE  ALT=\"sin+%28theta%29=y%2Fr\"   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%285%29%2F3 ALIGN=MIDDLE  ALT=\"sin+%28theta%29=-sqrt%285%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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