document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=444866>Question 444866</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i derive the formulas for sin(theta over 2) , Cos(Theta over 2) and Tan(Theta over 2) from a figure </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #306581 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=306581\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C0%2C10%2C0%2C10%2C%0D%0A%0D%0A%0D%0Atriangle%282%2C2%2C8%2C2%2C8%2C9%29%2C%0D%0Alocate%282%2C2%2CA%29%2C%0D%0Alocate%288%2C2%2CC%29%2C%0D%0Alocate%288%2C9%2CB%29%2C%0D%0Aline%282%2C2%2C8%2C4.5%29%2C%0D%0Alocate%288%2C4.5%2CD%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\angle BAC = \theta\">, you know that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin{\frac{\theta}{2}} = \frac{CD}{AD}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos{\frac{\theta}{2}} = \frac{BD}{AD}\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \tan{\frac{\theta}{2}} = \frac{CD}{BD}\">\r<BR>\n" );
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document.write( "Also, you know that AD is an angle bisector, so the following ratio holds:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{AB}{BD} = \frac{AC}{CD}\">\r<BR>\n" );
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document.write( "Try combining these to derive the half-angle formulas. </SPAN>\n" );
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