document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972990>Question 972990</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are given the value of tan &#952;. Is it possible to find the values of all the other trigonometric functions without finding the actual measure of the angle &#952;? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #595266 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=595266\">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( "Trick question.  Except for cotangent, you cannot find THE value of the other functions, you can only find all possible values of the other functions.\r<BR>\n" );
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document.write( "For example, let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \tan\theta\ =\ x\">\r<BR>\n" );
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document.write( "Then from the definition of tangent,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin\theta}{\cos\theta}\ =\ x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin\theta\ =\ x\cos\theta\">\r<BR>\n" );
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document.write( "Square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2\theta\ =\ x^2\cos^2\theta\">\r<BR>\n" );
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document.write( "Use the Pythagorean Identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ \cos^2\theta\ =\ x^2\cos^2\theta\">\r<BR>\n" );
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document.write( "Then do a bunch of algebra that I will let you verify on your own:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\theta\ =\ \pm\sqrt{\frac{1}{x^2\ +\ 1}}\">\r<BR>\n" );
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document.write( "Similarly\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \tan\theta\ =\ x\ \Rightarrow\ \sin\theta\ =\ \pm\sqrt{\frac{x^2}{x^2\ +\ 1}\">\r<BR>\n" );
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document.write( "And the other three functions are just the reciprocals of the ones we now know.\r<BR>\n" );
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document.write( "However, for any given non-zero value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \tan\theta\">, there are two values for sine, cosine, secant, and cosecant.  So, depending on exactly what your instructor meant by <i>\"...find the values of all the other trigonometric functions without finding the actual measure of the angle\"</i>, the answer to your question is either yes or no.\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\r<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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