document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117290>Question 1117290</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If sin &#945; = 4/5 and cos &#946; = -5/13 for &#945; in Quadrant I and &#946; in Quadrant II, find cos(&#945; - &#946;). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #732342 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=732342\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\(\varphi\,-\,\psi\)\ =\ \sin\(\varphi\)\sin\(\psi\)\ +\ \cos\(\varphi\)\cos\(\psi\)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin\(\alpha\)\ =\ \frac{4}{5}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin\(\alpha\)\ \in\ QI\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2\(\alpha\)\ =\ \frac{16}{25}\ \Right\ \cos^2\(\alpha\)\ =\ 1\ -\ \frac{16}{25}\ =\ \frac{9}{25}\ \Right\ \cos\(\alpha\)\ =\ \pm\sqrt{\frac{9}{25}}\ =\ \pm\frac{3}{5}\">\r<BR>\n" );
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document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \cos\(\varphi\)\ \geq\ 0\"> for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \varphi\ \in\ QI\">\r<BR>\n" );
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document.write( "Hence <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \cos\(\alpha\)\ =\ \frac{3}{5}\">\r<BR>\n" );
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document.write( "Similarly, and I leave the arithmetic to you:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin\(\beta\)\ =\ \frac{12}{13}\">\r<BR>\n" );
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document.write( "Therefore:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\(\alpha\,-\,\beta\)\ =\ \(\frac{4}{5}\)\(\frac{12}{13}\)\ +\ \(\frac{3}{5}\)\(-\frac{5}{13}\)\">\r<BR>\n" );
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document.write( "The rest is just arithmetic.  Mind your signs.\r<BR>\n" );
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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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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