document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965062>Question 965062</A>: <I><SPAN STYLE=\"word-break: break-all;\"> evaluate the expression given that sina=-4/5with pi<a<3pi/2 and cos b=5/13 with 0<b<pi/2\r<BR>\n" );
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document.write( "1. cos(a-b)\r<BR>\n" );
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document.write( "2.sin(a+b)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589915 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=589915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> evaluate the expression given that sina=-4/5with pi<a<3pi/2 and cos b=5/13 with 0<b<pi/2<BR>\n" );
document.write( "***<BR>\n" );
document.write( "sina=-4/5 (Q3)<BR>\n" );
document.write( "cosa=-3/5<BR>\n" );
document.write( "cosb=5/13 (Q1)<BR>\n" );
document.write( "sinb=12/13<BR>\n" );
document.write( "..<BR>\n" );
document.write( "1. cos(a-b)=cosa*cosb+sina*sinb=-3/5*5/13+-4/5*12/13=-15/65-48/65=-63/65<BR>\n" );
document.write( "2.sin(a+b)=sina*cosb+cosa*sinb=-4/5*5/13+-3/5*12/13=-20/65-36/65=-56/65<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "sina=-4.5<BR>\n" );
document.write( "a=233.13&#730;<BR>\n" );
document.write( "cosb=5/13<BR>\n" );
document.write( "b=67.38&#730;<BR>\n" );
document.write( "a-b=165.75&#730;<BR>\n" );
document.write( "a+b=300.51&#730;<BR>\n" );
document.write( "cos(a-b)=cos(165.75)&#8776;-0.9692<BR>\n" );
document.write( "exact value as computed above=-63/65&#8776;-0.9692<BR>\n" );
document.write( "sin(a+b)=sin(300.51)&#8776;-0.8615<BR>\n" );
document.write( "exact value as computed above=-56/65&#8776;-0.8615 </SPAN>\n" );
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