document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=602906>Question 602906</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I need help with my homework. We are learning about the sum and difference of identities.\r<BR>\n" );
document.write( "\n" );
document.write( "Here is the problem:\r<BR>\n" );
document.write( "\n" );
document.write( "What is the value of sin(A-b) if tan A = 9/40 and A is in the first quadrant, while cos B = -4/5 and B is in the third quadrant?\r<BR>\n" );
document.write( "\n" );
document.write( "I really don't get this homework. What is up with A and B? Do we need to plot the graph as well? It's confusing me. I'm sorry if I'm asking stupid questions, I missed our class today, you see. I hope someone can explain this to me properly so I'll catch up with the lesson. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #380496 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=380496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A is an angle and they tell you it is in the first quadrant and that the tangent is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{9}{40}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B is another angle.  You are given that this angle is in the third quadrant and that the cosine is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -\frac{4}{5}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "They want to subtract the measure of angle B from the measure of angle A and then take the sine of the difference.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For such an operation you need the difference formula for sine:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(A\ -\ B)\ =\ \sin(A)\cos(A)\ -\ \cos(A)\sin(B)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remember that tangent is sine over cosine, so:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin(A)}{\cos(A)}\ =\ \frac{9}{40}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 40\sin(A)\ =\ 9\cos(A)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Square both sides:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1600\sin^2(A)\ =\ 81\cos^2(A)\"> \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the Pythagorean Identity and substitute:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1600\(1\ -\ cos^2(A)\ =\ 81\cos^2(A)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Collect like terms:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2(A)\ =\ \frac{1600}{1681}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Take the positive (remember, QI) square root:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos(A)\ =\ \frac{40}{41}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(A)\ =\ \frac{81}{1681}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Again, the positive square root:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(A) =\ \frac{9}{41}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Similarly you can get from <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos(B)\ =\ -\frac{3}{5}\"> to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin(B)\ =\ -\frac{4}{5}\">.  QIII, both sine and cosine are negative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now you have the four values you need to plug into:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(A\ -\ B)\ =\ \sin(A)\cos(A)\ -\ \cos(A)\sin(B)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can do your own arithmetic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then, for futher study, here are the other three formulas you will need:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF=\"http://oakroadsystems.com/twt/sumdiff.htm\">Sum and Difference Formulas</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<div  DISABLED_style= \"text-align:center\"><a  rel=nofollow HREF=\"http://outcampaign.org/\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png\" border=\"0\" alt=\"The Out Campaign: Scarlet Letter of Atheism\" width=\"143\" height=\"122\" /></a></div><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );