document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=467644>Question 467644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the sin(a+b) if tan(a) = 7/24 where a is in the third quadrant and cos (b)= -12/13 where b is in the second quadrant </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #320941 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=320941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the sin(a+b) if tan(a) = 7/24 where a is in the third quadrant and cos (b)= -12/13 where b is in the second quadrant<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Identity required: sin(a+b)=sin a cos b +cos a sin b<BR>\n" );
document.write( "so we must find sin a, sin b, cos a and cos b<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Given: tan (a) =7/24 in quadrant III<BR>\n" );
document.write( "This gives a hypotenuse=&#8730;(24^2+7^2)=&#8730;625=25<BR>\n" );
document.write( "In quadrant III, both sin and cos are <0<BR>\n" );
document.write( "sin a=-7/25<BR>\n" );
document.write( "cos a=-24/25<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Given: cos (b)=-12/13 in quadrant II (cos<0, sin>0)<BR>\n" );
document.write( "Opposite leg=&#8730;(13^2-12^2)=&#8730;25=5<BR>\n" );
document.write( "Sin b=5/13<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(a+b)=(-7/25)(-12/13)+(-24/25)(5/13)<BR>\n" );
document.write( "=.2585-.3692=.1107<BR>\n" );
document.write( "..<BR>\n" );
document.write( "ans: sin(a+b)=.1107 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );