PHALIN THAKKAR
Why zero and 180 degrees agree
Why does changing the field sign preserve intensity, and how should angular errors be reported?
Note 5 · Explanatory note
Analytical result · Hypothetical examples are not physical measurements.
For an analyzer:
At 30°, cos²30° = 0.75. At 210°, cos210° ≈ −0.8660; the exact squared value is again 0.75. Use an approximation sign for the rounded cosine and calculate with full precision.
This periodicity also changes how an estimation error should be computed. A fitted axis of 1° is only 2° from a true axis of 179°, because the axis repeats after 180°. Ordinary subtraction would produce −178°.
Use the wrapped signed error:
Its result is in radians if the inputs are in radians. Convert to degrees after evaluation.