Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. Abbreviation of arcsine.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. the inverse function of the sine; the angle that has a sine equal to a given number
Etymologies
Examples

I was once told that the gradient on a road sign is not arctan but rather arcsin  i.e. 10% is 1m up for 10m on the slope.

The green theme was adapted from a template by Viktor Persson at arcsin.

And, he apparently is well educated, as he knows the number pi and trigonometrical functions like sin, cos, tan, arcsin, arccos, arctan and the functions sqrt and exp.
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Again we use the refraction formula, this time to ﬁ nd the angle 3, relative to the normal N2r, at which the ray of red light exits the second surface of the prism: sin 3 = sin 40: 79518 ¼ 1: 52000 = 1: 00000 sin 3 = 0: 653356 ¼ 1: 52000 sin 3 ¼ 0: 653356 Â 1: 52000 ¼ 0: 993101 3 ¼ arcsin 0: 993101 ¼ 83: 26598

When a light ray passes through a boundary from a medium having an index of refraction r into a medium having an index of refraction s, the critical angle, c, is given by the formula: c ¼ arcsin ðs = rÞ What does this formula tell us about rays striking a boundary where r ¼ s/2?

When a light ray passes through a boundary from a medium having an index of refraction r into a medium having an index of refraction s, the critical angle, c, is given by the formula: c ¼ arcsin ðs = rÞ Suppose c ¼ 1 rad, and s ¼ 1.225.

The former expression refers to the inverse sine of x, or the arcsine of x (arcsin x); but the latter expression means the reciprocal of the sine of x, that is, 1/(sin x).

Plug in the numbers to the equation for critical angle, c: c ¼ arcsin ðs = rÞ ¼ arcsin ð1: 00 = 1: 33Þ ¼ arcsin 0: 752 ¼ 48: 88 Remember that the angles in all these situations are de ﬁ ned with respect to the normal to the surface, not with respect to the plane of the surface.

If we are operating on some variable x, the arcsine of x is denoted sinÀ1 (x) or arcsin (x) 48 CHAPTER 3 Graphs and Inverses Fig. 310.

When a light ray passes through a boundary from a medium having an index of refraction r into a medium having an index of refraction s, the critical angle, c, is given by the formula: c ¼ arcsin ðs = rÞ What does this formula tell us about rays striking a boundary where r ¼ 2s?
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