document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884194>Question 884194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the 3rd quadrant , if sin A = -3/5   and  sec B = -13/12 then tan (A-B) = ?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534181 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=534181\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the 3rd quadrant , if sin A = -3/5 and sec B = -13/12 then tan (A-B) = ?<BR>\n" );
document.write( "***<BR>\n" );
document.write( "sinA=-3/5(working with a (3-4-5) reference right triangle in quadrant III)<BR>\n" );
document.write( "cosA=-4/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cosB=1/secB<BR>\n" );
document.write( "cosB=-12/13(working with a (5-12-13) reference right triangle in quadrant III)<BR>\n" );
document.write( "sinB=-5/13<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(A-B)=sinA*cosB-cosA*sinB=(-3/5)*(-12/13)-(-4/5)*(-5/13)=36/65-20/65=16/65<BR>\n" );
document.write( "cos(A-B)=cosA*cosB+sinA*sinB=(-4/5)*(-12/13)+(-3/5)*(-5/13)=48/65+15/65=63/65<BR>\n" );
document.write( "tan(A-B)=sin(A-B)/cos(A-B)=16/63<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "sinA=-3/5<BR>\n" );
document.write( "A&#8776;216.87&#730;<BR>\n" );
document.write( "cosB=-12/13<BR>\n" );
document.write( "B&#8776;202.62&#730;<BR>\n" );
document.write( "A-B&#8776;14.25<BR>\n" );
document.write( "tan(A-B)&#8776;tan(14.25)&#8776;0.2539…<BR>\n" );
document.write( "exact value=16/63&#8776;0.2539… </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );