document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=831733>Question 831733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use a double- or half-angle identity to find the exact value of each trigonometric expression below if csc x = 4 and 90 degrees < x < 180 degrees\r<BR>\n" );
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document.write( "a) sin x/2\r<BR>\n" );
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document.write( "b) cos x/2 \r<BR>\n" );
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document.write( "c) tan x/2<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501609 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=501609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use a double- or half-angle identity to find the exact value of each trigonometric expression below if csc x = 4 and 90 degrees < x < 180 degrees<BR>\n" );
document.write( "a) sin x/2<BR>\n" );
document.write( "b) cos x/2<BR>\n" );
document.write( "c) tan x/2<BR>\n" );
document.write( "***<BR>\n" );
document.write( "cscx=4<BR>\n" );
document.write( "sinx=1/4<BR>\n" );
document.write( "cosx=-&#8730;(1-sin^2x)=-&#8730;(1-(1/16))=-&#8730;(15/16)=-&#8730;15/4<BR>\n" );
document.write( "note: cos<0,sin>0 in quadrant II<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(x/2)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2Bcos%28x%29%29%2F2%29=sqrt%28%281%2Bsqrt%2815%29%2F4%29%2F2%29=sqrt%28%284%2Bsqrt%2815%29%29%2F8%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos(x/2)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281-cos%28x%29%29%2F2%29=sqrt%28%281-sqrt%2815%29%2F4%29%2F2%29=sqrt%28%284-sqrt%2815%29%29%2F8%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "tan(x/2)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sin%28x%29%29%2F%281-cos%28x%29%29=%281%2F4%29%2F%28%281-sqrt%2815%29%2F4%29%29=%281%2F4%29%2F%28%284-sqrt%2815%29%29%2F4%29=1%2F%284-sqrt%2815%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "Calculator check:<BR>\n" );
document.write( "sinx=1/4<BR>\n" );
document.write( "x&#8776;165.52&#730; in quadrant II<BR>\n" );
document.write( "x/2&#8776;82.76&#730;<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(x/2)&#8776;sin(82.76)&#8776;0.9920..<BR>\n" );
document.write( "exact value=&#8730;(4+&#8730;15)/8&#8776;0.9920..<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos(x/2)&#8776;cos(82.76)&#8776;0.1260..<BR>\n" );
document.write( "exact value=&#8730;(4-&#8730;15)/8&#8776;0.1260..<BR>\n" );
document.write( "..<BR>\n" );
document.write( "tan(x/2)=tan(82.76)&#8776;7.872..<BR>\n" );
document.write( "exact value=1/(4-&#8730;15)&#8776;7.872.. </SPAN>\n" );
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