document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185013>Question 1185013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the dimensions and the area of the largest rectangle that can be fit under the graph of y = sin(x), 0 <= x <= π, if one side of the rectangle lies on the positive x-axis. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815710 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=815710\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The height of the rectangle will be y=sin(x); by symmetry, to length of the rectangle will be (pi-2x).  So the area of the rectangle will be<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28pi-2x%29sin%28x%29 ALIGN=MIDDLE  ALT=\"A=%28pi-2x%29sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We could try to solve the problem by finding where the derivative of the area function is zero; however, the equation we end up with can't be solved by purely algebraic methods.<br><BR>\n" );
document.write( "So we might as well find the answer by using our graphing calculator or similar tool to find the maximum value of the area function.<br><BR>\n" );
document.write( "ANSWERS: (to a few decimal places)<BR>\n" );
document.write( "x=0.7104613<BR>\n" );
document.write( "height sin(x) = 0.652184<BR>\n" );
document.write( "length pi-2x = 1.72067<BR>\n" );
document.write( "area (pi-2x)*sin(x) = 1.122192<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );