arcsin love

# arcsin

## Definitions

• n. Abbreviation of arcsine.

• n. the inverse function of the sine; the angle that has a sine equal to a given number

arc- +‎ sin

## 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.

Which idiot came up with percentage-based gradient signs

• 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.

Linux Journal - The Original Magazine of the Linux Community

• 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.