document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125840>Question 1125840</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that the exact value of sin pi/10 = -1+&#8730;5 divided by 4, for each question calculate the exact value of the expression. You may leave nested radicals in your answer, but rationalize any denominaters. <BR>\n" );
document.write( "sin pi/5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742177 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=742177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F5%29+=+sin%28%282%2A%28pi%2F10%29%29%29+=+2sin%28pi%2F10%29cos%28pi%2F10%29 ALIGN=MIDDLE  ALT=\"sin%28pi%2F5%29+=+sin%28%282%2A%28pi%2F10%29%29%29+=+2sin%28pi%2F10%29cos%28pi%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28pi%2F10%29+=+sqrt%281-sin%28pi%2F10%29%5E2%29 ALIGN=MIDDLE  ALT=\"cos%28pi%2F10%29+=+sqrt%281-sin%28pi%2F10%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute (2) into (1)  and use the given value of sin(pi/10) to get<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28pi%2F5%29+=+2%28%28-1%2Bsqrt%285%29%29%2F4%29%2Asqrt%281-%28%28-1%2Bsqrt%285%29%29%2F4%29%5E2%29 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=%28%28-1%2Bsqrt%285%29%29%2F2%29%2Asqrt%281-%286-2%2Asqrt%285%29%29%2F16%29 ALIGN=MIDDLE  ALT=\"%28%28-1%2Bsqrt%285%29%29%2F2%29%2Asqrt%281-%286-2%2Asqrt%285%29%29%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-1%2Bsqrt%285%29%29%2F2%29%2A%28sqrt%2810%2B2%2Asqrt%285%29%29%2F4%29 ALIGN=MIDDLE  ALT=\"%28%28-1%2Bsqrt%285%29%29%2F2%29%2A%28sqrt%2810%2B2%2Asqrt%285%29%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-1%2Bsqrt%285%29%29%2Asqrt%2810%2B2%2Asqrt%285%29%29%29%2F8 ALIGN=MIDDLE  ALT=\"%28%28-1%2Bsqrt%285%29%29%2Asqrt%2810%2B2%2Asqrt%285%29%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Evaluating sin(pi/5) and that expression on a scientific calculator gives identical results, confirming the correctness of the expression. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );