document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035159>Question 1035159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the value for sin(x/2) if the following conditions hold tan(x)=-4/3 and x is in quadrant IV </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649813 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=649813\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the value for sin(x/2) if the following conditions hold tan(x)=-4/3 and x is in quadrant IV<BR>\n" );
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document.write( "tan = y/x<BR>\n" );
document.write( "r = sqrt(y^2 + x^2) = 5<BR>\n" );
document.write( "sin(x) = y/r = -4/5<BR>\n" );
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document.write( "sin^2(x/2) = (1 - cos(x))/2 *****  Much simpler than the sin(x/2)<BR>\n" );
document.write( "cos(x) = x/r = 3/5 --- cosine is + in Q4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "sin^2(x/2) = (2/5)/2 = 1/5<BR>\n" );
document.write( "sin(x/2) = sqrt(1/5) = sqrt(5)/5 </SPAN>\n" );
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