Question 1201900
this appears to be in radians.
arccos(cos(-4pi/3)) = 2.094395102 radians.
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.
cos(-4pi/3) = -.5
arccos(-.5) = 2.094395102.


note that -4pi/3 is a negative angle.
to convert to a positive angle between 0 and 2pi radians, add 2pi radians to it until it goes positive.
you will get -4pi/3 + 2pi = 2.094395102 radians.
that is the an equivalent positive angle that has the same trig functions as the noriginal negative angle.
your expression then becomes:
arccos(cos(2.094395102)) = 2.094395102.


this is easier to see in degrees.
thd equivalent angle in degrees of -4pi/3 is equal to that * 180 / pi = -240 degrees.
the original expression then becomes arccos(cos(-240)).
the equivalent positive angle to -240 degrees is found by adding 360 to it until it becomes positive between 0 and 360 degrees.
-240 + 360 = 120 degrees.
the expression becomes arecos(cos(120)) degrees = 120 degrees.
cos(120) = -.5.
arccos -.5 = 120.


by equivalent angles, it is meant that they have the same trig function values.


trig functions for 120 degrees are:
sine = .8660254038
cosine = -.5
tangent = .1.732050808


trig functions for -240 degrees are:
sine = .8660254038
cosine = -.5
tangent = .1.732050808


note that the reference angle for 120 degrees is equal to 180 - 120 = 60 degrees.


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.


note also that sin(60) = .5 and cosinje(60) = sqrt(3)/2 which is equal to .8660254038.


your solution is that arccos(cos(-4pi/3)) = 2.094395102 radians.