document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80871>Question 80871</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write <BR>\n" );
document.write( "f(x) = cot  (arccos (x/16))<BR>\n" );
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document.write( "in a way which doesn't involve trigonometric or inverse trigonometric functions </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58017 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=58017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,<br />\r<BR>\n" );
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document.write( "I'll start you off and hopefully you can finish it yourself. Knowledge of trig identities will come in handy here, whenever I encounter things like this, I find it easier to write the problem in terms of sin and cos, so let's do that. You may know that cot(a)=cos(a)/sin(a), but if you didn't, the way I remember it is that cot(a)=1/tan(a) and that tan(a)=sin(a)/cos(a). However you remember it doesn't matter, but knowing your cot(), cosec(), sec() in terms of sin() and cos() is very important.<br />\r<BR>\n" );
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document.write( "Anyway, back to the problem, I'm going to let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?y=x/16\"> as otherwise we're bound to leave a 16 out somewhere and get in a mess. So we're now looking at:<br />\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\frac{\cos(\cos^{-1}(y))}{\sin(\cos^{-1}(y))}\">\r<BR>\n" );
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document.write( "The top line is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?y\"> right? Can you tell me why?<br />\r<BR>\n" );
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document.write( "The bottom line needs a little more work. The way to get rid of the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\cos^{-1}\"> is to take the cosine of it, like we did for the numerator. So we need a way of converting a sine to a cosine. There's a pretty good identity for that, I'm sure you've seen it:<br />\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\cos^2 + \sin^2 = 1\">\r<BR>\n" );
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document.write( "Rearrange that, to get sin as a function of cosine, then substitute into the bottom line.<br />\r<BR>\n" );
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document.write( "Once you've done that don't forget to rewrite it in terms of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x\">, and that's your answer.<br />\r<BR>\n" );
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document.write( "Once you've got it, or if you get stuck, post your answer/working and I can check/try to help.<br />\r<BR>\n" );
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document.write( "Kev </SPAN>\n" );
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