document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159222>Question 1159222</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use half-angle formulas to find the exact values.<BR>\n" );
document.write( "a. cos 15(degrees)<BR>\n" );
document.write( "b. sin 20(degress)30'\r<BR>\n" );
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document.write( "I got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/2 for a and -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >/2 for b which are wrong. What did I do wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782211 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=782211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'm not sure what part b is trying to say because the notation is a bit strange. \r<BR>\n" );
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document.write( "I'll show you how to do part a\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%2F2%29+=+sqrt%28+%281%2Bcos%28x%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28x%2F2%29+=+sqrt%28+%281%2Bcos%28x%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Half angle identity for cosine, when cosine is positive. Keep in mind that cos(15) is a positive value as the angle 15 degrees is in Q1 where cosine is positive.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2830%2F2%29+=+sqrt%28+%281%2Bcos%2830%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%2830%2F2%29+=+sqrt%28+%281%2Bcos%2830%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x = 30\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2815%29+=+sqrt%28+%281%2Bsqrt%283%29%2F2%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%2815%29+=+sqrt%28+%281%2Bsqrt%283%29%2F2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace cos(30) with sqrt(3)/2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2815%29+=+sqrt%28+%282%2F2%2Bsqrt%283%29%2F2%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%2815%29+=+sqrt%28+%282%2F2%2Bsqrt%283%29%2F2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 1 as 2/2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2815%29+=+sqrt%28+%28%282%2Bsqrt%283%29%29%2F2%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%2815%29+=+sqrt%28+%28%282%2Bsqrt%283%29%29%2F2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the upper fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2815%29+=+sqrt%28+%28%282%2Bsqrt%283%29%29%2F2%29%2A%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"cos%2815%29+=+sqrt%28+%28%282%2Bsqrt%283%29%29%2F2%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=cos%2815%29+=+sqrt%28+%282%2Bsqrt%283%29%29%2F4+%29 ALIGN=MIDDLE  ALT=\"cos%2815%29+=+sqrt%28+%282%2Bsqrt%283%29%29%2F4+%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=cos%2815%29+=+sqrt%28+2%2Bsqrt%283%29+%29%2Fsqrt%284%29 ALIGN=MIDDLE  ALT=\"cos%2815%29+=+sqrt%28+2%2Bsqrt%283%29+%29%2Fsqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2815%29+=+sqrt%28+2%2Bsqrt%283%29+%29%2F2 ALIGN=MIDDLE  ALT=\"cos%2815%29+=+sqrt%28+2%2Bsqrt%283%29+%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify sqrt(4) into 2. This is as simplified as it gets.\r<BR>\n" );
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document.write( "Side note: if you use a calculator, you should find<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2815%29+=+0.96592582628907 ALIGN=MIDDLE  ALT=\"cos%2815%29+=+0.96592582628907\"   DISABLED_style= \"max-width:90%; height:auto;\" > (make sure your calculator is in degree mode)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+2%2Bsqrt%283%29+%29%2F2+=+0.96592582628907 ALIGN=MIDDLE  ALT=\"sqrt%28+2%2Bsqrt%283%29+%29%2F2+=+0.96592582628907\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "both are approximations. Since we get the same approximation, this helps confirm the answer.\r<BR>\n" );
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document.write( "Another way to confirm the answer is to compute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+sqrt%282%2Bsqrt%283%29%29+%29%2F%282%29-cos%2815%29 ALIGN=MIDDLE  ALT=\"%28+sqrt%282%2Bsqrt%283%29%29+%29%2F%282%29-cos%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you should get zero as a result (or some very small number due to rounding error). I'm using the idea that if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+y ALIGN=MIDDLE  ALT=\"x+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y+=+0 ALIGN=MIDDLE  ALT=\"x-y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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