document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=966896>Question 966896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help!!!! Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u= 4/5. Now I know to make a triangle a^2+b^2=c^2. Then you get the missing line which is 3. From there sin(2u) and cos(2u) use the double Angle formula and get sin(2u)=-24/25 and cos(2u)=7/25. I even get how to solve the sin and cos of u/2 by using the half angle formulas but what I'm confused on is the positive and negative answers. I thought sin u/2=-&#8730;(10)/10 and cos u/2= 3(&#8730;(10)/10) but it's actually sin u/2=+&#8730;(10)/10 and cos u/2= -3(&#8730;(10)/10). I'm so confused. Shouldn't sin u/2 be - because it is in the fourth quadrant??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590924 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=590924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u= 4/5 in quadrant IV<BR>\n" );
document.write( "***<BR>\n" );
document.write( "cosu=4/5<BR>\n" );
document.write( "sinu=-3/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(2u)=2sinucosu=2*-3/5*4/5=-24/25<BR>\n" );
document.write( "cos(2u)=cos^2(u)-sin^(u)=16/25-9/25=7/25<BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28u%2F2%29=sqrt%28%281-cosu%29%2F2%29=sqrt%28%281-%284%2F5%29%2F2%29%29=sqrt%28%281%2F5%29%2F2%29=sqrt%281%2F10%29=sqrt%2810%29%2F10 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28u%2F2%29=-sqrt%28%281%2Bcosu%29%2F2%29=-sqrt%28%281%2B%284%2F5%29%2F2%29%29=-sqrt%28%289%2F5%29%2F2%29=-sqrt%289%2F10%29=-3%2Fsqrt%2810%29=-3sqrt%2810%29%2F10 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "cosu=4/5(Q4)<BR>\n" );
document.write( "u=323.13<BR>\n" );
document.write( "u/2=161.56<BR>\n" );
document.write( "2u=646.26<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(u/2)=sin(161.56)=0.3163<BR>\n" );
document.write( "exact value as computed=&#8730;10/10&#8776;0.3162<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos(u/2)=cos(161.56)=-0.9486<BR>\n" );
document.write( "exact value as computed=3&#8730;10/10&#8776;-0.9486<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(2u)=sin(646.26)=-0.9600<BR>\n" );
document.write( "exact value as computed=-24/25=-0.9600<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos(2u)=cos(646.26)=.2800<BR>\n" );
document.write( "exact value as computed=7/25=0.2800\r<BR>\n" );
document.write( "\n" );
document.write( "note: This is a revision of a solution submitted earlier because u was changed to be in quadrant IV  instead of quadrant I\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );