document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=461701>Question 461701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the exact value of sin ((22 1/2)degrees) using sum and difference? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316565 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=316565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Use the Half-Angle Formula for Sine which follows directly from the Double Angle Formula for Cosine which follows directly from the Sum Formula for Cosine.  See <a  rel=nofollow HREF=\"http://oakroadsystems.com/twt/double.htm<BR>\n" );
document.write( "\">Double Angle and Half Angle Formulas</a> for a complete discussion.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 22.5^\circ\ =\ \frac{45^\circ}{2}\">\r<BR>\n" );
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document.write( "And\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos(45^\circ)\ =\ \frac{\sqrt{2}}{2}\">\r<BR>\n" );
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document.write( "From the unit circle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png\">\r<BR>\n" );
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document.write( "Since the half-angle formula for sine is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin\left(\frac{\varphi}{2}\right)\ =\ \pm\sqrt{\frac{1\ -\ \cos(\varphi)}{2}}\">\r<BR>\n" );
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document.write( "where you select the sign based on the quadrant in which <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin\left(\frac{\varphi}{2}\right)\"> exists.\r<BR>\n" );
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document.write( "We can write, since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 22.5^\circ\"> is in the first quadrant:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin\left(22.5^\circ\right)\ =\ \sqrt{\frac{1\ -\ \frac{\sqrt{2}}{2}}{2}}\ =\ \frac{\sqrt{2\ -\ \sqrt{2}}}{2}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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