Cosine_error
Cosine error
Type of measurement error
Cosine error is a type of measurement error caused by the difference between the intended and actual directions in which a measurement is taken. Depending on the type of measurement, it either multiplies or divides the true value by the cosine of the angle between the two directions.
For small angles the resulting error is typically very small, since an angle needs to be relatively large for its cosine to depart significantly from 1.[1][2]
Approximate error sizes for a few example angles are:[3]
Angle | Error | |
10° | 1.5% | = 1 part in 65 or 66[4] |
1° | 0.015% | = 1 part in 6,600 |
0.1° | 0.00015% | = 1 part in 660,000 |
0.01° | 0.0000015% | = 1 part in 66,000,000 |
The error is equivalent to treating the hypotenuse and one of the other sides of a right-angled triangle as if they were equal; the cosine of the angle between them is the ratio[5] of their lengths.