document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201900>Question 1201900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate:\r<BR>\n" );
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document.write( "arccos[cos(-4pi/3)] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836462 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=836462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this appears to be in radians.<BR>\n" );
document.write( "arccos(cos(-4pi/3)) = 2.094395102 radians.<BR>\n" );
document.write( "simplest way to do it,if you don't know how to do it in one shot, is to find cos(-4pi/3) first and than find the arccos of that.<BR>\n" );
document.write( "cos(-4pi/3) = -.5<BR>\n" );
document.write( "arccos(-.5) = 2.094395102.\r<BR>\n" );
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document.write( "note that -4pi/3 is a negative angle.<BR>\n" );
document.write( "to convert to a positive angle between 0 and 2pi radians, add 2pi radians to it until it goes positive.<BR>\n" );
document.write( "you will get -4pi/3 + 2pi = 2.094395102 radians.<BR>\n" );
document.write( "that is the an equivalent positive angle that has the same trig functions as the noriginal negative angle.<BR>\n" );
document.write( "your expression then becomes:<BR>\n" );
document.write( "arccos(cos(2.094395102)) = 2.094395102.\r<BR>\n" );
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document.write( "this is easier to see in degrees.<BR>\n" );
document.write( "thd equivalent angle in degrees of -4pi/3 is equal to that * 180 / pi = -240 degrees.<BR>\n" );
document.write( "the original expression then becomes arccos(cos(-240)).<BR>\n" );
document.write( "the equivalent positive angle to -240 degrees is found by adding 360 to it until it becomes positive between 0 and 360 degrees.<BR>\n" );
document.write( "-240 + 360 = 120 degrees.<BR>\n" );
document.write( "the expression becomes arecos(cos(120)) degrees = 120 degrees.<BR>\n" );
document.write( "cos(120) = -.5.<BR>\n" );
document.write( "arccos -.5 = 120.\r<BR>\n" );
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document.write( "by equivalent angles, it is meant that they have the same trig function values.\r<BR>\n" );
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document.write( "trig functions for 120 degrees are:<BR>\n" );
document.write( "sine = .8660254038<BR>\n" );
document.write( "cosine = -.5<BR>\n" );
document.write( "tangent = .1.732050808\r<BR>\n" );
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document.write( "trig functions for -240 degrees are:<BR>\n" );
document.write( "sine = .8660254038<BR>\n" );
document.write( "cosine = -.5<BR>\n" );
document.write( "tangent = .1.732050808\r<BR>\n" );
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document.write( "note that the reference angle for 120 degrees is equal to 180 - 120 = 60 degrees.\r<BR>\n" );
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document.write( "note also that the reference angle for -240 degrees is the same, because -240 is equivalent to 120 degrees and the reference angle for 120 degrees is 60 degrees.\r<BR>\n" );
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document.write( "note also that sin(60) = .5 and cosinje(60) = sqrt(3)/2 which is equal to .8660254038.\r<BR>\n" );
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document.write( "your solution is that arccos(cos(-4pi/3)) = 2.094395102 radians.<BR>\n" );
document.write( " </SPAN>\n" );
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