document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=731793>Question 731793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let<BR>\n" );
document.write( "sin A =12/13<BR>\n" );
document.write( "with A in QII and<BR>\n" );
document.write( "sin B = &#8722; 15/17<BR>\n" );
document.write( "with B in QIII. Find sin(A + B), cos(A + B), and 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 #447337 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=447337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let<BR>\n" );
document.write( "sin A =12/13<BR>\n" );
document.write( "with A in Q2 and<BR>\n" );
document.write( "sin B = &#8722; 15/17<BR>\n" );
document.write( "with B in Q3. Find sin(A + B), cos(A + B), and tan(A + B).<BR>\n" );
document.write( "**<BR>\n" );
document.write( "let o=opposite side<BR>\n" );
document.write( "let a=adjacent side<BR>\n" );
document.write( "let h=hypotenuse<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin A =12/13=o/h<BR>\n" );
document.write( "o=12, h=13<BR>\n" );
document.write( "a=-&#8730;h^2-o^2)=-&#8730;(13^2-12^2)=-&#8730;(169-144)=-&#8730;25=-5<BR>\n" );
document.write( "cos A=a/h=-5/13<BR>\n" );
document.write( "tan A=o/a=-12/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sinB =-15/17=o/h<BR>\n" );
document.write( "o=-15, h=17<BR>\n" );
document.write( "a=-&#8730;h^2-o^2)=-&#8730;(17^2-15^2)=-&#8730;(289-225)=-&#8730;64=-8<BR>\n" );
document.write( "cos B=a/h=-8/17<BR>\n" );
document.write( "tan B=o/a=-15/-8=15/8<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(A+B)=(sinA*cosB)+(cosA*sinB)<BR>\n" );
document.write( "=(12/13)*(-8/17)+(-5/13*-15/17)<BR>\n" );
document.write( "=-96/221+75/221<BR>\n" );
document.write( "=-21/221<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos(A+B)=cosA*cosB)-(sinA*sinB)<BR>\n" );
document.write( "=(-5/13)*(-8/17)-(12/13*-15/17)<BR>\n" );
document.write( "=40/221+180/221<BR>\n" );
document.write( "=220/221<BR>\n" );
document.write( "..<BR>\n" );
document.write( "tan(A+B)=(tanA+tanB)/(1-tanA*tanB<BR>\n" );
document.write( "=(-12/5+15/8)/(1-(-12/5)(15/8))<BR>\n" );
document.write( "=(-96/40+75/40)/(1+180/40<BR>\n" );
document.write( "=(-21/40)/(220/40)<BR>\n" );
document.write( "=-21/220<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Check with calculator:<BR>\n" );
document.write( "sinA=12/13 in Q2<BR>\n" );
document.write( "A&#8776;112.62º<BR>\n" );
document.write( "sin B=-15/17 in Q3<BR>\n" );
document.write( "B&#8776;241.93º<BR>\n" );
document.write( "A+B&#8776;354.55º<BR>\n" );
document.write( "reference angle=5.45º in Q4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(A+B)=sin(354.55)=sin(5.45) in Q4&#8776;-0.0945...<BR>\n" );
document.write( "-21/221=&#8776;-0.0945... <BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos(A+B)=cos(354.55)=cos(5.45) in Q4&#8776;0.9954...<BR>\n" );
document.write( "220-221&#8776;0.9954...<BR>\n" );
document.write( "..<BR>\n" );
document.write( "tan(A+B)=tan(354.55)=tan(5.45) in Q4&#8776;-0.0954...<BR>\n" );
document.write( "-21/220&#8776;-0.0954...<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );