# Arcsin free online calculator

Online arcsin(x) calculator. Inverse sine calculator.

Enter value of x (between -1 and 1) and hit "Calculate" button

°

Sine calculator »

arcsin(x), sin-1(x), inverse sine function.

### Arcsin definition

The arcsine of x is defined as the inverse sine function of x when -1≤x≤1.

When the sine of y is equal to x:

sin y = x

Then the arcsine of x is equal to the inverse sine function of x, which is equal to y:

arcsin x = sin-1 x = y

#### Example

arcsin 1 = sin-1 1 = π/2 rad = 90°

### Arcsin rules

Rule nameRule
Sine of arcsinesin( arcsin x ) = x
Arcsine of sinearcsin( sin x ) = x+2kπ, when k∈ℤ (k is integer)
Arcsin of negative argumentarcsin(-x) = - arcsin x
Complementary anglesarcsin x = π/2 - arccos x = 90° - arccos x
Arcsin sumarcsin α + arcsin(β) = arcsin( α√(1-β2) + β√(1-α2) )
Arcsin differencearcsin α - arcsin(β) = arcsin( α√(1-β2) - β√(1-α2) )
Cosine of arcsine
Tangent of arcsine
Derivative of arcsine
Indefinite integral of arcsine

### Arcsin table

xarcsin(x)

arcsin(x)

(°)

-1-π/2-90°
-√3/2-π/3-60°
-√2/2-π/4-45°
-1/2-π/6-30°
00
1/2π/630°
2/2π/445°
3/2π/360°
1π/290°

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