document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=893601>Question 893601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Maclaurin expansion of sin x to find the value of sin 45 correct to four decimal places </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #541588 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=541588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Maclaurin series expansion is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=sum%28f%5E%28k%29%280%29%2A%28%28x-0%29%5Ek%2Fk%21%29%2Ck=0%2Cinfinity%29 ALIGN=MIDDLE  ALT=\"f%28x%29=sum%28f%5E%28k%29%280%29%2A%28%28x-0%29%5Ek%2Fk%21%29%2Ck=0%2Cinfinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5Ek ALIGN=MIDDLE  ALT=\"f%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the k-th derivative of the function.<BR>\n" );
document.write( "In this case,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=sin%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%281%29%28x%29=cos%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%281%29%28x%29=cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%282%29%28x%29=-sin%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%282%29%28x%29=-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%283%29%28x%29=-cos%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%283%29%28x%29=-cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%284%29%28x%29=sin%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%284%29%28x%29=sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%285%29%28x%29=cos%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%285%29%28x%29=cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%286%29%28x%29=-sin%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%286%29%28x%29=-sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then take the value of each at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=sin%280%29=0 ALIGN=MIDDLE  ALT=\"f%280%29=sin%280%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%281%29%280%29=cos%280%29=1 ALIGN=MIDDLE  ALT=\"f%5E%281%29%280%29=cos%280%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%282%29%280%29=-sin%280%29=0 ALIGN=MIDDLE  ALT=\"f%5E%282%29%280%29=-sin%280%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%283%29%280%29=-cos%280%29=-1 ALIGN=MIDDLE  ALT=\"f%5E%283%29%280%29=-cos%280%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%284%29%280%29=sin%280%29=0 ALIGN=MIDDLE  ALT=\"f%5E%284%29%280%29=sin%280%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%285%29%280%29=cos%280%29=1 ALIGN=MIDDLE  ALT=\"f%5E%285%29%280%29=cos%280%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%286%29%280%29=-sin%280%29=0 ALIGN=MIDDLE  ALT=\"f%5E%286%29%280%29=-sin%280%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Putting it all together,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29=0%2B1%28%28x-0%29%29%2F1%2B0-1%28%28x-0%29%5E3%29%2F3%21-0%2B1%2A%28x-0%29%5E5%2F5%21-0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You begin to see the pattern,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29=x-%28x%29%5E3%2F3%21%2B%28x%29%5E5%2F5%21-%28x%29%5E7%2F7%21 ALIGN=MIDDLE  ALT=\"sin%28x%29=x-%28x%29%5E3%2F3%21%2B%28x%29%5E5%2F5%21-%28x%29%5E7%2F7%21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So find the value of 45 degrees in radians,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%28%282%2Api%29%2F360%29=0.785398 ALIGN=MIDDLE  ALT=\"45%28%282%2Api%29%2F360%29=0.785398\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And substitute,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%280.785398%29=0.785398-%280.785398%29%5E3%2F3%21%2B%280.785398%29%5E5%2F5%21-%280.785398%29%5E7%2F7%21 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=sin%280.785398%29=0.707106 ALIGN=MIDDLE  ALT=\"sin%280.785398%29=0.707106\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I think that's pretty good compared to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2F2=0.707107 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2F2=0.707107\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%280.785398%29=0.7071 ALIGN=MIDDLE  ALT=\"sin%280.785398%29=0.7071\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );