document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=293364>Question 293364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hoe to find the exact value of cos(arcsin(-1/2) + arctan(2/3))= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #211830 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=211830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the exact value of cos(arcsin(-1/2) + arctan(2/3))<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Plot the points and assign the angles A and B<BR>\n" );
document.write( "A = arcsin(-1/2) = -30º<BR>\n" );
document.write( "cos(A) = sqrt(3)/2<BR>\n" );
document.write( "sin(A) = -1/2<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "B = arctan(2/3) <BR>\n" );
document.write( "gives the point (2,3), a distance of sqrt(13) from the Origin.<BR>\n" );
document.write( "cos(B) = 3sqrt(13)/13<BR>\n" );
document.write( "sin(B) = 2sqrt(13)/13<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "cos(A+B) = cos(A)cos(B) - sin(A)sin(B)<BR>\n" );
document.write( "= sqrt(3)/2 * 3sqrt(13)/13 - (-1/2)*2sqrt(13)/13<BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%2839%29%2F26+%2B+sqrt%2813%29%2F13 ALIGN=MIDDLE  ALT=\"3sqrt%2839%29%2F26+%2B+sqrt%2813%29%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "or, = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2813%29%2F26%29%2A%283sqrt%283%29+%2B+2%29 ALIGN=MIDDLE  ALT=\"%28sqrt%2813%29%2F26%29%2A%283sqrt%283%29+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );