document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032166>Question 1032166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If csc(theta)= -5/3 and theta has its terminal side in Quadrant III, find the exact value of tan(2theta). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646809 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=646809\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  If csc(theta)= -5/3 and theta has its terminal side in Quadrant III, find the exact value of tan(2theta). <BR>\n" );
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document.write( "csc = r/y = -5/3 in QIII where x and y are negative.<BR>\n" );
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document.write( "So r = 5 and y = -3<BR>\n" );
document.write( "Then x = -sqrt(r^2-y^2) = -sqrt(16) = -4<BR>\n" );
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document.write( "tan(t) = y/x = 3/4<BR>\n" );
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document.write( "tan(2*t) = 2tan(t)/[1-tan^2(t)] = 2(3/4)/[1-(9/16)] = (3/2)/(7/16) = 24/7<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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