document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=966988>Question 966988</A>: <I><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 where 3pi/2< u <2pi. 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 #590997 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=590997\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28u%29=4%2F5 ALIGN=MIDDLE  ALT=\"cos%28u%29=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28u%29%2Bsin%5E2%28u%29=1 ALIGN=MIDDLE  ALT=\"cos%5E2%28u%29%2Bsin%5E2%28u%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F25%2Bsin%5E2%28u%29=1 ALIGN=MIDDLE  ALT=\"16%2F25%2Bsin%5E2%28u%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28u%29=9%2F25 ALIGN=MIDDLE  ALT=\"sin%5E2%28u%29=9%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28u%29=0+%2B-+3%2F5 ALIGN=MIDDLE  ALT=\"sin%28u%29=0+%2B-+3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since it's Q4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28u%29=-3%2F5 ALIGN=MIDDLE  ALT=\"sin%28u%29=-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282u%29=2sin%28u%29cos%28u%29 ALIGN=MIDDLE  ALT=\"sin%282u%29=2sin%28u%29cos%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282u%29=2%28-3%2F5%29%284%2F5%29 ALIGN=MIDDLE  ALT=\"sin%282u%29=2%28-3%2F5%29%284%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282u%29=-24%2F25 ALIGN=MIDDLE  ALT=\"sin%282u%29=-24%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282u%29=cos%5E2%28u%29-sin%5E2%28u%29 ALIGN=MIDDLE  ALT=\"cos%282u%29=cos%5E2%28u%29-sin%5E2%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282u%29=%2816%2F25%29-%289%2F25%29 ALIGN=MIDDLE  ALT=\"cos%282u%29=%2816%2F25%29-%289%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282u%29=7%2F25 ALIGN=MIDDLE  ALT=\"cos%282u%29=7%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28u%2F2%29=0+%2B-+sqrt%28%281-cos%28u%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28u%2F2%29=0+%2B-+sqrt%28%281-cos%28u%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28u%2F2%29=0+%2B-+sqrt%28%281-4%2F5%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28u%2F2%29=0+%2B-+sqrt%28%281-4%2F5%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28u%2F2%29=0+%2B-+sqrt%28%281%2F5%29%2F2%29 ALIGN=MIDDLE  ALT=\"sin%28u%2F2%29=0+%2B-+sqrt%28%281%2F5%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28u%2F2%29=0+%2B-+sqrt%281%2F10%29 ALIGN=MIDDLE  ALT=\"sin%28u%2F2%29=0+%2B-+sqrt%281%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28u%2F2%29=0+%2B-+sqrt%2810%29%2F10 ALIGN=MIDDLE  ALT=\"sin%28u%2F2%29=0+%2B-+sqrt%2810%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in Q4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2F2 ALIGN=MIDDLE  ALT=\"u%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be in Q2, where sine is positive.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28u%2F2%29=sqrt%2810%29%2F10 ALIGN=MIDDLE  ALT=\"sin%28u%2F2%29=sqrt%2810%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28u%2F2%29=0+%2B-+sqrt%28%281%2Bcos%28u%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28u%2F2%29=0+%2B-+sqrt%28%281%2Bcos%28u%29%29%2F2%29\"   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=0+%2B-+sqrt%28%281%2B4%2F5%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28u%2F2%29=0+%2B-+sqrt%28%281%2B4%2F5%29%2F2%29\"   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=0+%2B-+sqrt%28%289%2F5%29%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28u%2F2%29=0+%2B-+sqrt%28%289%2F5%29%2F2%29\"   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=0+%2B-+3%2Fsqrt%2810%29%29 ALIGN=MIDDLE  ALT=\"cos%28u%2F2%29=0+%2B-+3%2Fsqrt%2810%29%29\"   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=0+%2B-+%283%2F10%29sqrt%2810%29+%29 ALIGN=MIDDLE  ALT=\"cos%28u%2F2%29=0+%2B-+%283%2F10%29sqrt%2810%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Again since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in Q4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2F2 ALIGN=MIDDLE  ALT=\"u%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be in Q2, where cosine is negative.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28u%2F2%29=-%283%2F10%29sqrt%2810%29 ALIGN=MIDDLE  ALT=\"cos%28u%2F2%29=-%283%2F10%29sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );