document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=372386>Question 372386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please explain how to find all solutions of sin(x/2)+cosx-1=0?  I have been out of school for quite some time and I don't remember how to do this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #265305 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=265305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From double -angle identity, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cosx+=+1+-+2%28sin%28x%2F2%29%29%5E2 ALIGN=MIDDLE  ALT=\"cosx+=+1+-+2%28sin%28x%2F2%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  By direct substitution, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29%2Bcosx-1=+sin%28x%2F2%29+%2B+1+-+2%28sin%28x%2F2%29%29%5E2+-+1+=+sin%28x%2F2%29+-+2%28sin%28x%2F2%29%29%5E2+=+sin%28x%2F2%29%2A%281+-+2sin%28x%2F2%29%29+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >. Hence <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29+=+0 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+2sin%28x%2F2%29+=+0 ALIGN=MIDDLE  ALT=\"1+-+2sin%28x%2F2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  (The 2nd is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%2F2%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"sin%28x%2F2%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
document.write( "From the 1st equation we get x = 0 degrees, or 360 degrees.  From the second, we get x = 60 degrees, or 300 degrees.\r<BR>\n" );
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document.write( "****The solution given by the author below says that I have given ONLY TWO solutions, when I have given FOUR, namely 0, 60, 300, or 360 degrees.  If he had read my ENTIRE solution he should HAVE REALIZED that I was going for solutions between 0 and 360 degrees, inclusive.  I have left it to asker to just find the OTHER INFINITE solutions for his consideration.**** </SPAN>\n" );
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