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 n72π
Note that if you rotate 2π 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
72π 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 2π radians =360o≡1 full cycle
Assumption: rotation is anticlockwise:
So 72π radians is (72π÷2π)=74 cycles=134cycles.
Assuming you start at the standard point of 0o, you end up at the same point as34 cycles
In radian measure this becomes
34×360o=270o=34×2π=32π.radians. This is the same as−12π radians
In this solution I have assigned negative to be
clockwise rotation and obviously positive to be anticlockwise
