document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890647>Question 890647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch a right triangle corresponding to the trigonometric function of the acute angle &#952;. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of &#952;.<BR>\n" );
document.write( "cot &#952; = 9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539200 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the relationships are as follows:<BR>\n" );
document.write( "see the diagram at the bottom.\r<BR>\n" );
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document.write( "sin(A) = y/z\r<BR>\n" );
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document.write( "cos(A) = x/z\r<BR>\n" );
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document.write( "tan(A) = y/x\r<BR>\n" );
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document.write( "cot(A) = 1/tan(A) = x/y\r<BR>\n" );
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document.write( "sec(A) = 1/cos(A) = z/x\r<BR>\n" );
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document.write( "csc(A) = 1/sin(a) = z/y\r<BR>\n" );
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document.write( "you are given that cot(A) is equal to 9\r<BR>\n" );
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document.write( "that means that cot(a) = x/y = 9/1 which means that x is equal to 9 and y is equal to 1.\r<BR>\n" );
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document.write( "the pythagorean theorem states that z^2 = x^2 + y^2.\r<BR>\n" );
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document.write( "that means that z^2 = 9^2 + 1^2 which means that z^2 = 82.\r<BR>\n" );
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document.write( "that means that z = sqrt(82)\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = 9<BR>\n" );
document.write( "y = 1<BR>\n" );
document.write( "z = sqrt(82)\r<BR>\n" );
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document.write( "plug these numbers into your equations and  you should get the answer you are looking for after you follow the rules for simplification.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "sin(A) = y/z = 1 / sqrt(82) = sqrt(82) / 82\r<BR>\n" );
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document.write( "cos(A) = x/z = 9 / sqrt(82) = (9 * sqrt(82) / 82\r<BR>\n" );
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document.write( "tan(A) = y/x = 1 / 9\r<BR>\n" );
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document.write( "cot(A) = 1/tan(A) = x/y = 9 / 1 = 9\r<BR>\n" );
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document.write( "sec(A) = 1/cos(A) = z/x = sqrt(82) / 9\r<BR>\n" );
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document.write( "csc(A) = 1/sin(a) = z/y = sqrt(82) / 1 = sqrt(82)\r<BR>\n" );
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document.write( "here's a picture of your triangle.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/080305.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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