document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1077680>Question 1077680</A>: <I><SPAN STYLE=\"word-break: break-all;\">  find the Fourier expansion of the function: f(t)=sin^3t and f(t)=(2sint&#8722;cost)^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692491 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=692491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That's really beyond the scope of this website. <BR>\n" );
document.write( "You need to work on integrating to get your coefficients.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B0%5D=%281%2F%282pi%29%29%2Aint%28f%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%2Aint%28sin%5E3%28t%29%2Cdt%2C0%2C2pi%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=%281%2F%282pi%29%29%2Aint%28f%28t%29%2Acos%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%2Aint%28cos%28t%29%2Asin%5E3%28t%29%2Cdt%2C0%2C2pi%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Actually all of the a coefficients are zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D=%281%2F%282pi%29%29%2Aint%28f%28t%29%2Asin%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%2Aint%28sin%5E4%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%28%283pi%29%2F4%29=3%2F8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B2%5D=%281%2F%282pi%29%29%2Aint%28f%28t%29%2Asin%5E2%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%2Aint%28sin%5E5%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%28%283pi%29%2F4%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B3%5D=%281%2F%282pi%29%29%2Aint%28f%28t%29%2Asin%5E3%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%2Aint%28sin%5E6%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%28%285pi%29%2F8%29=5%2F16 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B4%5D=%281%2F%282pi%29%29%2Aint%28f%28t%29%2Asin%5E4%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%2Aint%28sin%5E7%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%28%283pi%29%2F4%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B5%5D=%281%2F%282pi%29%29%2Aint%28f%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%2Aint%28sin%5E8%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%28%2835pi%29%2F64%29=35%2F128 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That's a start on the first one. <BR>\n" );
document.write( "You can find the formula also by plugging in,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bn%5D=+%281%2F%282pi%29%29%2Aint%28f%28t%29%2Asin%5E%28n%29%28t%29%2Cdt%2C0%2C2pi%29=%281%2F%282pi%29%29%2Aint%28sin%5E%28n%2B3%29%28t%29%2Cdt%2C0%2C2pi%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and solving for when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is even.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );