Inverse trigonometric function: Arcsine (arcsin)

Definition

Arcsine (arcsin) is the inverse trigonometric function.

Arcsinus x defined as the function inverse to the sine x, at -1≤x≤1.

If the sine of the angle у is х (without y = x), which means the arcsine x equals y:

arcsin x = sin^-1 x = y

Note: without^-1x means inverse sine, not sine to the power -1.

For example:

arcsin 1 = sin^-1 1 = 90° (π/2 rad)

arcsine plot

The arcsine function is written as y = arcsin (x). The graph in general looks like this:-1≤x≤1, -π/2≤y≤π/2):

Arcsine properties

The main properties of the arcsine with formulas are presented in tabular form below.

Arcsine table