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" );
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document.write( "Here is the problem:\r<BR>\n" );
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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" );
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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 #380491 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=380491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is the problem:\r<BR>\n" );
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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" );
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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?<BR>\n" );
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document.write( "Here's the one I just did with the same angles.<BR>\n" );
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document.write( "If tan A = 9/40, A is in the first quadrant, cos B = -4/5, B is in the third quadrant, find the value of cos(A+B)<BR>\n" );
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document.write( "Find the cos(A)<BR>\n" );
document.write( "Tan = y/x<BR>\n" );
document.write( "Plot the point (40,9)<BR>\n" );
document.write( "--> hyp = sqrt(40^2 + 9^2) = 41<BR>\n" );
document.write( "cos(A) = x/hyp = 9/41<BR>\n" );
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document.write( "cos(A + B) = cosA*cosB - sinA*sinB (from Wikipedia)<BR>\n" );
document.write( "Find sin(A) and sin(B)<BR>\n" );
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document.write( "sin(A) = y/hyp = 40/41<BR>\n" );
document.write( "sin(B) = -3/5 in Q3 (it's the 3, 4, 5 triangle)<BR>\n" );
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document.write( "cos(A + B) = cosA*cosB - sinA*sinB<BR>\n" );
document.write( "= (9/41)*(-4/5) - (40/41)*(-3/5)<BR>\n" );
document.write( "= -36/205 + 120/205<BR>\n" );
document.write( "= 84/205<BR>\n" );
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document.write( "Use some of the values found in the previous problem:<BR>\n" );
document.write( "sin(A-b) = sin(A)cos(B) - cos(A)sin(B)<BR>\n" );
document.write( "= (40/41)*(-4/5) - (9/41)*(-3/5)<BR>\n" );
document.write( "= -200/205 + 27/205<BR>\n" );
document.write( "= -173/205<BR>\n" );
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document.write( "What is up with A and B?<BR>\n" );
document.write( "Angles A & B are measured from the x-axis counter-clockwise.  All angles on the x-y plane are measured that way.<BR>\n" );
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document.write( "Do we need to plot the graph as well?  You don't have to if you don't want to.<BR>\n" );
document.write( "Not much to graph, just a point for each angle.<BR>\n" );
document.write( "For A draw a line from the Origin to (40,9)<BR>\n" );
document.write( "For B it's to (-3,4)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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