document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=632146>Question 632146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given cos(2a)=-17/18 and<BR>\n" );
document.write( " 0<2a< pi/2<BR>\n" );
document.write( "find exact values <BR>\n" );
document.write( "of the six trigonometric functions.<BR>\n" );
document.write( " Note: you cannot us decimals in your answer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #398040 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=398040\">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( "First thing to note is that since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 0\ <\ 2a\ <\ \frac{\pi}{2}\">, a simple division operation shows that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 0\ <\ a\ <\ \frac{\pi}{4}\">, forcing <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a\"> to be a first quadrant angle, hence all six basic trigonometric functions will be positive.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos(2\varphi)\ \equiv\ \cos^2(\varphi)\ -\ \sin^2(\varphi)\">\r<BR>\n" );
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document.write( "So\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2(a)\ -\ \sin^2(a)\ =\ -\frac{17}{18}\">\r<BR>\n" );
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document.write( "Since we know that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2(\varphi)\ +\ \sin^2(\varphi)\ \equiv\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ 2\sin^2(a)\ =\ -\frac{17}{18}\">\r<BR>\n" );
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document.write( "And then a little algebra music, Sammy:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(a)\ =\ \pm\frac{\sqrt{35}}{6}\">\r<BR>\n" );
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document.write( "From which we discard the negative root because of the interval analysis earlier to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin(a)\ =\ \frac{\sqrt{35}}{6}\">\r<BR>\n" );
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document.write( "And likewise:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\cos^2(a)\ -\ 1\ =\ -\frac{17}{18}\">\r<BR>\n" );
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document.write( "From which we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos(a)\ =\ \frac{1}{6}\">\r<BR>\n" );
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document.write( "Use the following identities to get the other four functions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \tan(\varphi)\ \equiv\ \frac{\sin(\varphi)}{\cos(\varphi)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cot(\varphi)\ \equiv\ \frac{1}{\tan{\varphi}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sec(\varphi)\ \equiv\ \frac{1}{\cos{\varphi}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \csc(\varphi)\ \equiv\ \frac{1}{\sin{\varphi}\">\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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