document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205267>Question 205267</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given cos(x)= (-1/10) with 90 degrees<x<180 degrees Find cos ((1/2)x)\r<BR>\n" );
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document.write( "I solved this...\r<BR>\n" );
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document.write( "cos^2(theta/2)= (1/2)(1+cos(theta))\r<BR>\n" );
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document.write( "             =((1/2) ((10/10)-(1/10))<BR>\n" );
document.write( "             =(1/2)(9/10)<BR>\n" );
document.write( "             =9/20<BR>\n" );
document.write( "cos (theta/2)=sqroot (9/20)<BR>\n" );
document.write( "             = 3/ (sqroot20)<BR>\n" );
document.write( "              =(3(sqroot20))/20<BR>\n" );
document.write( "              =(3*2sqroot5)/20<BR>\n" );
document.write( "              =(3sqroot5)/10<BR>\n" );
document.write( "I marked it as NEGATIVE because it is in the second quadrant but it is marked wrong. However, when I submit positive (3sqroot5)/10 it marks it right. Why does it remain positive even though it is in the second quadrant? <BR>\n" );
document.write( "               <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 #154940 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=154940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given cos(x)= (-1/10) with 90 degrees I solved this... <BR>\n" );
document.write( "cos^2(theta/2)= (1/2)(1+cos(theta)) <BR>\n" );
document.write( "=((1/2) ((10/10)-(1/10))<BR>\n" );
document.write( "=(1/2)(9/10)<BR>\n" );
document.write( "=9/20<BR>\n" );
document.write( "cos (theta/2)=sqroot (9/20)<BR>\n" );
document.write( "= 3/ (sqroot20)<BR>\n" );
document.write( "=(3(sqroot20))/20<BR>\n" );
document.write( "=(3*2sqroot5)/20<BR>\n" );
document.write( "=(3sqroot5)/10<BR>\n" );
document.write( "I marked it as NEGATIVE because it is in the second quadrant but it is marked wrong. However, when I submit positive (3sqroot5)/10 it marks it right. Why does it remain positive even though it is in the second quadrant? \r<BR>\n" );
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document.write( "It accepts the positive answer because you are calculating the<BR>\n" );
document.write( "cos of (theta/2).  Although theta is in the 2nd quadrant, theta/2<BR>\n" );
document.write( "is in the 1st quadrant.<BR>\n" );
document.write( "================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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