document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=520169>Question 520169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find sinalpha if tan(alpha/2)=1/root2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #345975 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=345975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find sin(alpha) if tan(alpha/2) = 1/sqrt(2)<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Since tan(alpha/2) = y/x = 1/sqrt(2),<BR>\n" );
document.write( "y = 1 when x = sqrt(2)<BR>\n" );
document.write( "So, r = sqrt[1^2+(sqrt(2))^2] = sqrt(1+2) = sqrt(3)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Then sin(alpha/2) = y/r = 1/sqrt(3)<BR>\n" );
document.write( "and cos(alpha/2) = x/r = sqrt(2)/sqrt(3) = (1/3)sqrt(6)<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Finally, sin(alpha) = sin(2(alpha/2)) = 2sin(alpha/2)*cos(alpha/2)<BR>\n" );
document.write( "= 2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= (2sqrt(6)/(3*sqrt(3))<BR>\n" );
document.write( "------<BR>\n" );
document.write( "= (2/3)[sqrt(18)/3]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= (2/3)sqrt(2)<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "====================\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );