document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998930>Question 998930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (theta) is in the third quadrant and sin(theta)=-(3/5), what is cos(1/2 theta)? Give your answer as a fraction in simplest from. <BR>\n" );
document.write( "-half angle formulas </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616685 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52909)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=616685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "1. &nbsp;First calculate\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281+-+sin%5E2%28theta%29%29 ALIGN=MIDDLE  ALT=\"sqrt%281+-+sin%5E2%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281+-+%28-3%2F5%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%281+-+%28-3%2F5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2825-9%29%2F25%29 ALIGN=MIDDLE  ALT=\"sqrt%28%2825-9%29%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2F25%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F5 ALIGN=MIDDLE  ALT=\"-4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The sign is \"minus\" because the angle &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp;&nbsp; is in the third quadrant.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. &nbsp;Next, &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28%281%2F2%29theta%29 ALIGN=MIDDLE  ALT=\"cos%28%281%2F2%29theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281+%2B+cos%5E2%28theta%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%281+%2B+cos%5E2%28theta%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;See the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometric-functions-of-half-argument.lesson>Trigonometric functions of half argument</A>&nbsp; in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It gives &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28%281%2F2%29theta%29 ALIGN=MIDDLE  ALT=\"cos%28%281%2F2%29theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%28%281+%2B+cos%5E2%28theta%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"-sqrt%28%281+%2B+cos%5E2%28theta%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%28%281+%2B+%28-4%2F5%29%5E2%29%2F2%29 ALIGN=MIDDLE  ALT=\"-sqrt%28%281+%2B+%28-4%2F5%29%5E2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%28%2825+%2B+16%29%2F%282%2A25%29%29 ALIGN=MIDDLE  ALT=\"-sqrt%28%2825+%2B+16%29%2F%282%2A25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2841%2F50%29 ALIGN=MIDDLE  ALT=\"-sqrt%2841%2F50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The sign is &nbsp;\"minus\" &nbsp;because the angle &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha%2F2 ALIGN=MIDDLE  ALT=\"alpha%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp;&nbsp; lies in the second quadrant.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );