The problem with trig is that unless the range is defined there are multiple answers as the cycles just keep on going. So technically it should be written as #n 7/2pi#
Note that if you rotate #2pi# radians you have completed 1 cycle and you are back where you started. I suppose that if you are talking about work done (physics) the number of rotations is important. However, if you are talking purely numbers then it is not so critical
#7/2pi# radians is actually defining the number of rotations. However, just being interested in the angular measure of rotational state you would have to take into account that #2pi" radians "= 360^o -= 1 # full cycle
#color(brown)("Assumption: rotation is anticlockwise:")#
So #7/2 pi # radians is #(7/2 pi divide 2 pi)=7/4# cycles#=1 3/4#cycles.
Assuming you start at the standard point of #0^o,# you end up at the same point as#3/4# cycles
In radian measure this becomes
#3/4 times 360^o = 270^o = 3/4 times 2 pi =3/2 pi color(white)(.)#radians. This is the same as# -1/2 pi# radians
#color(blue)("In this solution I have assigned negative to be")#
#color(blue)("clockwise rotation and obviously positive to be anticlockwise")#
