document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=690398>Question 690398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if cos(a) is 2/3 and sin(b) is 4/5 what is cos(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 #426278 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=426278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if cos(a) is 2/3 and sin(b) is 4/5 what is cos(a+b)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos a=2/3=adj side/hypotenuse<BR>\n" );
document.write( "opp side=&#8730;(3^2-2^2)=&#8730;(9-4)=&#8730;5<BR>\n" );
document.write( "sin a=&#8730;5/3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin b=4/5 (3-4-5 right triangle)<BR>\n" );
document.write( "cos b=3/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos(a+b)=cos a cos b -sin a sin b<BR>\n" );
document.write( "=2/3*3/5 -&#8730;5/3*4/5<BR>\n" );
document.write( "=6/15-4&#8730;5/15<BR>\n" );
document.write( "=(6-4&#8730;5)/15<BR>\n" );
document.write( "..<BR>\n" );
document.write( "calculator check:<BR>\n" );
document.write( "a=cos^1(2/3)&#8776;.8411<BR>\n" );
document.write( "b=sin^-1(4/5)=.9273<BR>\n" );
document.write( "cos(a+b)=cos(1.7684)=-0.1962..<BR>\n" );
document.write( "(6-4&#8730;5)/15=-0.1962.. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );