document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155308>Question 155308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (Please Help...midnight deadline!)I really need to understand this type of problem (I'll give 2 examples):\r<BR>\n" );
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document.write( "Simplify the expressions below. \r<BR>\n" );
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document.write( "(a) For -00 < t < 00,<BR>\n" );
document.write( "cos( tan^-1( t ))=____________\r<BR>\n" );
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document.write( "(b) For -1 < w < 1,<BR>\n" );
document.write( "cot( cos^-1( w ))+____________\r<BR>\n" );
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document.write( "I understand that cos=adj/hyp and tan=opp/adj, but what is the relationship of cos to tan^-1 in this problem?  I also understant limiting the range (ie. b), just not the relationship between cot and cos.\r<BR>\n" );
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document.write( "Appreciate any help I can get ...thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114362 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=114362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simplify the expressions below. <BR>\n" );
document.write( "(a) For -00 < t < 00,<BR>\n" );
document.write( "cos( tan^-1( t ))=____?________<BR>\n" );
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document.write( "Consider tan^-1(t)<BR>\n" );
document.write( "This is \"the angle whose tangent is \"t\".<BR>\n" );
document.write( "Let the angle be theta.<BR>\n" );
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document.write( "Draw a right triangle.<BR>\n" );
document.write( "Let the base be 1 and the height be \"t\"<BR>\n" );
document.write( "Then the angle opposite \"t\" is theta.<BR>\n" );
document.write( "Verify for yourself that tan(theta) = t/1 = t<BR>\n" );
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document.write( "Using Pythagoras, the hypotenuse = sqrt(1^2 + t^2) = sqrt(1+t^2)<BR>\n" );
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document.write( "Ans: Then cos(theta) + cos(tan^-1(t)) = t/sqrt(1+t^2)<BR>\n" );
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document.write( "(b) For -1 < w < 1,<BR>\n" );
document.write( "cot( cos^-1( w ))+_____?_______ <BR>\n" );
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document.write( "Let cos^-1(w) = theta<BR>\n" );
document.write( "Draw a right triangle.<BR>\n" );
document.write( "Let the base be \"w\".<BR>\n" );
document.write( "Then the hypotenuse = 1<BR>\n" );
document.write( "Theta is the angle opposite the remaining side.<BR>\n" );
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document.write( "Verify for yourself that cos(theta) = w/1 = w<BR>\n" );
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document.write( "Use Pythagoras to find the side opposite theta:<BR>\n" );
document.write( "Let that unknown side be \"y\"<BR>\n" );
document.write( "1 = w^2 + y^2<BR>\n" );
document.write( "y = sqrt(1-w^2)<BR>\n" );
document.write( "Ans: Then cot(theta) = w/[sqrt(1-w^2)]<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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