document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=428535>Question 428535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I get the correct answer to these types of problems? <BR>\n" );
document.write( " It says to evaluate by use of the reference angle (arc), if applicable. \r<BR>\n" );
document.write( "\n" );
document.write( "cos(8pi/3)<BR>\n" );
document.write( "another is sin (5pi/3). <BR>\n" );
document.write( "How do I find these using the ref angle? thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297831 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=297831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do I get the correct answer to these types of problems? <BR>\n" );
document.write( "It says to evaluate by use of the reference angle (arc), if applicable. <BR>\n" );
document.write( "cos(8pi/3)<BR>\n" );
document.write( "another is sin (5pi/3). <BR>\n" );
document.write( "How do I find these using the ref angle?<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cos(8pi/3)<BR>\n" );
document.write( "Think (8pi/3) as 3+2/3 pi<BR>\n" );
document.write( "For each pi,you rotate the the terminating side 180 deg cc starting from the initial side at zero deg.<BR>\n" );
document.write( "So, for 3 pi, you complete one rotation plus 180 deg which puts the terminating side at 180 deg, but you still have 2/3 pi to go which is two pi/3 (60 deg) or 120 deg. The terminating side is now at 300 (180+120) deg which makes a reference angle of 60 deg with the x-axis in the 4th quadrant.  Hence, Cos(8pi/3)=1/2.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin (5pi/3)<BR>\n" );
document.write( "Think (5pi/3) as 1+2/3 pi<BR>\n" );
document.write( "In this case you rotate 1 pi to 180 deg with two pi/3 or 120 deg to go. This puts the terminating side at 300 deg,with the same reference angle as the cos above. Hence, Sin (5pi/3)=-sqrt(3)/2 (sin is negative in the 4th quadrant) </SPAN>\n" );
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