document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=963649>Question 963649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please solve this equation exactly.  \r<BR>\n" );
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document.write( "sin(arccos(3/5) - arctan(5/12)) =  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588774 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=588774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please solve this equation exactly. <BR>\n" );
document.write( "sin(arccos(3/5) - arctan(5/12)) =<BR>\n" );
document.write( "***<BR>\n" );
document.write( "let reference angle x=arccos(3/5)<BR>\n" );
document.write( "cosx=3/5<BR>\n" );
document.write( "sinx=4/5<BR>\n" );
document.write( "let reference angle y=arctan(5/12)<BR>\n" );
document.write( "cosy=12/13<BR>\n" );
document.write( "siny=5/13<BR>\n" );
document.write( "Identity: sin(x-y)=sinxcosy-cosxsiny=4/5*12/13-3/5*5/13=48/65-15/65=33/65<BR>\n" );
document.write( "sin(arccos(3/5) - arctan(5/12)) =33/65<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "arccos(3/5)&#8776;53.13&#730;<BR>\n" );
document.write( "arctan(5/12)&#8776;22.62&#730;<BR>\n" );
document.write( "53.13-22.62=30.51&#730;<BR>\n" );
document.write( "sin(30.51)&#8776;0.5077<BR>\n" );
document.write( "exact value as computed above=33/65&#8776;0.5077<BR>\n" );
document.write( " </SPAN>\n" );
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