document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=881256>Question 881256</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of sin (x+y) if sin x = 4/5 in Quadrant II and tan y = 12/5 in Quadrant III. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #532106 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=532106\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of sin (x+y) if sin x = 4/5 in Quadrant II and tan y = 12/5 in Quadrant III.<BR>\n" );
document.write( "***<BR>\n" );
document.write( "Identity:sin(x+y)=sinx*cosy+cosx*siny<BR>\n" );
document.write( "sinx=4/5, (3-4-5 reference right triangle in quadrant II in which sin>0, cos<0.)<BR>\n" );
document.write( "cosx=-3/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "tany=12/5 (5-12-13  reference right triangle in quadrant III in which sin<0, cos<0.)<BR>\n" );
document.write( "siny=-12/13<BR>\n" );
document.write( "cosy=-5/13<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(x+y)=4/5*-5/13+-3/5*-12/13=-20/65+36/65=16/65<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Calculator check:<BR>\n" );
document.write( "sinx=4/5 in Q2<BR>\n" );
document.write( "x&#8776;126.87&#730;<BR>\n" );
document.write( "tany=12/5 in Q3<BR>\n" );
document.write( "y&#8776;247.38&#730;<BR>\n" );
document.write( "x+y &#8776;374.25&#730;<BR>\n" );
document.write( "sin(x+y)=sin(374.2&#730;)&#8776;0.2461…<BR>\n" );
document.write( "Exact value=16/65&#8776;0.2461… </SPAN>\n" );
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