Angle Measurement

Following are the rules and formulae for angle measurements:

  1. Angle measurements greater than zero represent counter-clockwise measurements/rotation. Angle measurements lesser than zero represent clockwise measurements/rotation.
  2. Angle measurements/Rotations are modular 360 arithmatic. This means the angular calculations wrap around to zero after reaching \(\pm 359\)°. For e.g. a measurement/rotation of \(\pm 727\)° is actually a measurement of \(\pm 7\)°.
  3. Every counter-clockwise measurement/rotation has a corresponding clockwise measurement/rotation and vice versa. The following table illustrates this formula with examples:
    Measurement/Rotation TypeCorresponding measurement/rotation given byExample
    Counter-Clockwise of/by \(\theta\) Clockwise of/by \((\theta \bmod 360) - 360\) If Counter-Clockwise = 732°
    \(\Rightarrow\) Actual Counter-Clockwise=\((732 \bmod 360)\)=12°
    \(\Rightarrow\) Clockwise = 12° - 360° = -348°
    Clockwise of/by \(\theta\) Counter-Clockwise of/by \((\theta \bmod 360) + 360\) If Clockwise = -732°
    \(\Rightarrow\) Actual Clockwise=\((-732 \bmod 360)\)=-12°
    \(\Rightarrow\) Counter-Clockwise = -12° + 360° = 348°