document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1007340>Question 1007340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give sin(a) =8/9,<BR>\n" );
document.write( "pi/2< a < pi,<BR>\n" );
document.write( "Find the exact value of sin(a/2)\r<BR>\n" );
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document.write( "I tried solving it but I got stuck in some part.<BR>\n" );
document.write( "Here is my step for solving it.\r<BR>\n" );
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document.write( "Do pythagoream theorem to find cos (a)<BR>\n" );
document.write( "sin(a)=8/9 = y/r<BR>\n" );
document.write( "y=8, r=9\r<BR>\n" );
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document.write( "r^2=x^2+y^2<BR>\n" );
document.write( "9^2=x^2+8^2<BR>\n" );
document.write( "81=x^2+64<BR>\n" );
document.write( "sqrt(17)=x\r<BR>\n" );
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document.write( "cost=x/r=sqrt(17)/9\r<BR>\n" );
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document.write( "use double angle formula, sin(x/2)= +/- sqrt((1-costx)/2)<BR>\n" );
document.write( "sin(x/2)= +/- sqrt((1-sqrt((17)/9))/2)<BR>\n" );
document.write( "sin(x/2)= +/- sqrt((9/9-sqrt(17)/9))/2), I am stuck here. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623283 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=623283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%29+=+8%2F9 ALIGN=MIDDLE  ALT=\"sin%28a%29+=+8%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%29+=+%28sqrt%2817%29%29%2F%289%29 ALIGN=MIDDLE  ALT=\"cos%28a%29+=+%28sqrt%2817%29%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So you are correct there.\r<BR>\n" );
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document.write( "Start with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2+%3C+a+%3C+pi ALIGN=MIDDLE  ALT=\"pi%2F2+%3C+a+%3C+pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Multiply every side by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4+%3C+a%2F2+%3C+pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F4+%3C+a%2F2+%3C+pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F2 ALIGN=MIDDLE  ALT=\"a%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is larger than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4 ALIGN=MIDDLE  ALT=\"pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > but smaller than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This places angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F2 ALIGN=MIDDLE  ALT=\"a%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in quadrant 1. So <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;\" > is positive. So we only use the \"plus\" version of the formula (NOT the minus, NOT the plus/minus)\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+=+sqrt%28%281-cos%28a%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29+=+sqrt%28%281-cos%28a%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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+=+sqrt%28%281-%28sqrt%2817%29%29%2F%289%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29+=+sqrt%28%281-%28sqrt%2817%29%29%2F%289%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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+=+sqrt%28%289%2F9-%28sqrt%2817%29%29%2F%289%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29+=+sqrt%28%289%2F9-%28sqrt%2817%29%29%2F%289%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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+=+sqrt%28%28%289-sqrt%2817%29%29%2F%289%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29+=+sqrt%28%28%289-sqrt%2817%29%29%2F%289%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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+=+sqrt%28%28%289-sqrt%2817%29%29%2F%289%29%29%2A%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29+=+sqrt%28%28%289-sqrt%2817%29%29%2F%289%29%29%2A%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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+=+sqrt%28%289-sqrt%2817%29%29%2F%2818%29%29 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29+=+sqrt%28%289-sqrt%2817%29%29%2F%2818%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Exact value\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+=+0.52051760426961 ALIGN=MIDDLE  ALT=\"sin%28a%2F2%29+=+0.52051760426961\"   DISABLED_style= \"max-width:90%; height:auto;\" > Approximate value (use a calculator)\r<BR>\n" );
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