document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111358>Question 1111358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the length of a shadow cast by a sundial with a 3 foot tall gnomon is given by I(0) = 3 cot 0, where 0 is the angle of the sun above the eastern horizon. (0°&#8804;0&#8804; 180°)<BR>\n" );
document.write( "a. sketch a graph for the function. <BR>\n" );
document.write( "b. identify the asymptotes and interpret what they represent in th contex of the problem. <BR>\n" );
document.write( "c. for what values of 0 does the rod cast a 3 foot shadow? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #726337 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=726337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The cotangent is undefined at 0 degrees<BR>\n" );
document.write( "The shadow is infinitely long at 0 degrees (sun is at horizon) and at 180 degrees.<BR>\n" );
document.write( "It casts a 3 foot shadow at 45 and 135 degrees, because cot x= tan x=1<BR>\n" );
document.write( "It casts no shadow at 90 degrees (local noon), because at least this design will have the sun highest in the sky (90 degrees from horizon).  Note: this has to be a special kind of sundial, since the sun is directly overhead and casting no shadow only at certain time of year between the Tropics of Cancer and Capricorn.\r<BR>\n" );
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document.write( "The cotangent function is the tangent shifted 90 degrees, the way the sine and cosine functions are shifted. </SPAN>\n" );
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