document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965366>Question 965366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of the following under the given conditions.\r<BR>\n" );
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document.write( "if tan(x)= -4/3\r<BR>\n" );
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document.write( "and (pi/2)< x < pi\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "if sin(y)= 2/3\r<BR>\n" );
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document.write( "and 0< y < (pi/2)\r<BR>\n" );
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document.write( "find tan(x+y)<BR>\n" );
document.write( "show work and state exact value </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590146 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=590146\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of the following under the given conditions. <BR>\n" );
document.write( "if tan(x)= -4/3 <BR>\n" );
document.write( "and (pi/2)< x < pi <BR>\n" );
document.write( "and <BR>\n" );
document.write( "if sin(y)= 2/3 <BR>\n" );
document.write( "and 0< y < (pi/2) <BR>\n" );
document.write( "find tan(x+y)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "tanx=-4/3 ((3-4-5) reference right triangle in quadrant II)<BR>\n" );
document.write( "sinx=4/5<BR>\n" );
document.write( "cosx=-3/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "siny=2/3<BR>\n" );
document.write( "cosy=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281-sin%5E2%28y%29%29=sqrt%281-4%2F9%29=sqrt%285%2F9%29=sqrt%285%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%281-sin%5E2%28y%29%29=sqrt%281-4%2F9%29=sqrt%285%2F9%29=sqrt%285%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(x+y)=sinx*cosy+cosx*siny=4/5*&#8730;5/3+-3/5*2/3=4&#8730;5/15-6/15=(4&#8730;5-6)/15<BR>\n" );
document.write( "cos(x+y)=cosx*cosy-sinx*siny=-3/5*&#8730;5/3-4/5*2/3=-3&#8730;5/15-8/15=-(3&#8730;5+8)/15<BR>\n" );
document.write( "tan(x+y)=sin(x+y)/cos(x+y)=-(4&#8730;5-6)/(3&#8730;5+8)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "tanx=-4/3 (Q2)<BR>\n" );
document.write( "x=126.87&#730;<BR>\n" );
document.write( "siny=2/3 (Q1)<BR>\n" );
document.write( "y=41.81&#730;<BR>\n" );
document.write( "x+y=168.68<BR>\n" );
document.write( "tan(x+y)=tan(168.68)&#8776;-0.2002<BR>\n" );
document.write( "exact value as computed above=-(4&#8730;5-6)/(3&#8730;5+8)&#8776;-0.2002 </SPAN>\n" );
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