document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=735077>Question 735077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question.\r<BR>\n" );
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document.write( "Let g : N -> {+-cos(x), +-sin(x)} be defined by\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28n%29=%28d%5E%28n%29%2Fdx%5E%28n%29%29sin%28x%29 ALIGN=MIDDLE  ALT=\"g%28n%29=%28d%5E%28n%29%2Fdx%5E%28n%29%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a)Find a description of g(n) without using the differential operator.<BR>\n" );
document.write( "b)What is the 101st derivative of sinx? That is find g(101).\r<BR>\n" );
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document.write( "I have no idea where to start or how to do a). But I think once I have a) it might be easier to understand and work out b). But I thought I would still ask both. Thank you for your assistance in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #449282 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=449282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's look at sin(x) first.<BR>\n" );
document.write( "y=sin(x)<BR>\n" );
document.write( "y'(x)=cos(x)<BR>\n" );
document.write( "y''(x)=-sin(x)<BR>\n" );
document.write( "y'''(x)=-cos(x)<BR>\n" );
document.write( "y''''(x)=sin(x), so at the 4th derivative, we're back to sin(x)\r<BR>\n" );
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document.write( "n=1,5,9,13,..., derivative=cos(x)<BR>\n" );
document.write( "n=2,6,10,14,..., derivative=-sin(x)<BR>\n" );
document.write( "n=3,7,11,15,..., derivative=-cos(x)<BR>\n" );
document.write( "n=4,8,12,16,..., derivative=sin(x)\r<BR>\n" );
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document.write( "g(101) = cos(x)<BR>\n" );
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