document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=921229>Question 921229</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of the trigonometric expression given that <BR>\n" );
document.write( "sin u =5/13<BR>\n" );
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document.write( "cos v = &#8722;3/5<BR>\n" );
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document.write( " (Both u and v are in Quadrant II.)<BR>\n" );
document.write( "tan(u + v) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558900 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=558900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let A = u and B = v\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "sine of A = 5/13<BR>\n" );
document.write( "cosine of B = -3/5\r<BR>\n" );
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document.write( "both angles are in the second quadrant.\r<BR>\n" );
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document.write( "use the pythagorean formula to solve for the missing leg of each triangle.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "side opposite A = 5<BR>\n" );
document.write( "side adjacent A = -12<BR>\n" );
document.write( "hypotenuse A = 13\r<BR>\n" );
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document.write( "side opposite B = 4<BR>\n" );
document.write( "side adjacent B = -3<BR>\n" );
document.write( "hypotenuse B = 5\r<BR>\n" );
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document.write( "the side adjacent is negative in both triangles because they are both in the second quadrant where the value of x is negative while the value of y is positive.\r<BR>\n" );
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document.write( "now that you know the sides, you can solve for tangent of A and tangent of B.\r<BR>\n" );
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document.write( "tangent of A will be equal to 5 / -12 which is equal to -5/12.\r<BR>\n" );
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document.write( "tangent of B will be equal to 4 / -3 which is equal to -4/3.\r<BR>\n" );
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document.write( "tangent of A+B is equal to (tangent of A plus tangent of B) divided by (1 - tangent of A * tangent of B).\r<BR>\n" );
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document.write( "plug values in for the words and you get:\r<BR>\n" );
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document.write( "tangent of A plus B = ((-5/12) - (4/3)) divided by (1 - (-5/12 * -4/3)\r<BR>\n" );
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document.write( "do the arithmetic and this turns out to be:\r<BR>\n" );
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document.write( "tangent of A plus B = -1.75 / .4444444 which is equal to -3.9375.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "you can translate this back to u and v by letting u = A and v = B and you get:\r<BR>\n" );
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document.write( "tan(u+v) = -3.9375.\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
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