Arcsin

Arcsin can be used to calculate an angle from the length of the opposite side and the length of the hypotenuse. : Arccos can be used to calculate an angle from the length of the adjacent side and the length of the hypotenuse.

At the surfaces of the prism, Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin(sin (θ) / n).

If θ measures elevation from the reference plane instead of inclination from the zenith the arccos above becomes an arcsin, and the cos θ and sin θ below become switched.

Later, the system was further improved by use of an arcsine-based modulator that included a 1-0.52E term in the denominator of the arcsin generator equation.

The principal inverses are usually defined as: : The notations sin −1 and cos −1 are often used for arcsin and arccos, etc. When this notation is used, the inverse functions could be confused with the multiplicative inverses of the functions.