document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=907355>Question 907355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Excet velu of sin22.5? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #550312 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=550312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you are looking for the exact value of sin(22.5), you would do that as follows.\r<BR>\n" );
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document.write( "2 * 22.5 = 45<BR>\n" );
document.write( "since you know that the sin of 45 is sqrt(2)/2, you can use the pythagorean identity for a half angle formula to find the exact value of sin(22.5).\r<BR>\n" );
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document.write( "the half angle formula is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = plus or minus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281-cos%28a%29%29%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%28%281-cos%28a%29%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a = 45 degrees.<BR>\n" );
document.write( "cos(a) = sqrt(2)/2\r<BR>\n" );
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document.write( "replace cos(a) in the equation with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = plus or minus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281-sqrt%282%29%2F2%29%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%281-sqrt%282%29%2F2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this can be simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = plus or minus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%282-sqrt%282%29%29%2F2%29%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%282-sqrt%282%29%29%2F2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which can be further simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = plus or minus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%282-sqrt%282%29%29%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%28%282-sqrt%282%29%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which can be even further simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = plus or minus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%282-sqrt%282%29%29%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%28%282-sqrt%282%29%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since your angle is in the first quadrant, then your solution will be positive.\r<BR>\n" );
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document.write( "your solution is sin(22.5) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%282-sqrt%282%29%29%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%28%282-sqrt%282%29%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can confirm with your calculator.\r<BR>\n" );
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document.write( "using the calculator, sin(22.5) = .3826834324\r<BR>\n" );
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document.write( "also using the calculator, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%282-sqrt%282%29%29%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%28%282-sqrt%282%29%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .3826834324\r<BR>\n" );
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document.write( "most of the double and half angle formulas you need in high school trigonometry can be found in the following reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://regentsprep.org/Regents/math/algtrig/ATT14/formulalesson.htm\" target = \"_blank\">http://regentsprep.org/Regents/math/algtrig/ATT14/formulalesson.htm</a> </SPAN>\n" );
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