# Arcsin Calculator

Online arcsin(x) calculator. Inverse sine calculator.

For example, If the sine of 30° is 0.5:

sin(30°) = 0.5

Then the arcsine of 0.5 is 30°:

arcsin(0.5) = sin-1(0.5) = 30°

### Arcsine table

y x = arcsin(y)
-1 -90° -π/2
-0.8660254 -60° -π/3
-0.7071068 -45° -π/4
-0.5 -30° -π/6
0 0
0.5 30° π/6
0.7071068 45° π/4
0.8660254 60° π/3
1 90° π/2

Here we discuss list of online math calculators that help us for doing calculation easily.

### Arcsin Calculator

Arcsin is the inverse of the sine. It is normally represented by arcsin(θ) or sin-1(θ).Use arcsine calculator to easily calculate the arcsine of a number. Online arcsine calculation tool with output in degrees or radians. Supports input of decimal numbers (0.5, 6, -1, etc.) and fractions (1/4, 2/3, 4/3, 1/3 etc.).

Arcsine definition

The arcsine function is the inverse function of y = sin(x).

arcsin(y) = sin-1(y) = x + 2kπ

For every

k = {...,-2,-1,0,1,2,...}

For example, If the sine of 30° is 0.5:

sin(30°) = 0.5

Then the arcsine of 0.5 is 30°:

arcsin(0.5) = sin-1(0.5) = 30°

How to use the arcsin (x) calculator?

Enter x as a real number, within the domain of arcsin such that -1 ≤ x ≤ 1, and the number of decimal places desired then press "enter". Two answers are displayed: one in radians and the second in degrees.

What is arcsine?

Arcsine is an inverse of the sine function. In other words, it helps to find the angle of a triangle which has a know value of sine. As sine's codomain for real numbers is [−1, 1] , we can only calculate arcsine for numbers in that interval.

Sine is a periodic function, so there are multiple numbers that have the same sine value. For example sin(0) = 0, but also sin(π) = 0, sin(2π) = 0, sin(-π) = 0 and sin(-326π) = 0. Therefore, if somebody wants to calculate arcsin(0), the answer can be 0, 2π (360°) or -π (-180°), to name a few options! All of them are correct, but we usually only give one number called the principal value.

Arcsin(x) is the most common notation, as sin-1x may lead to confusion (because sin-1x ≠ 1/sin(x) ). The abbreviation asin in usually used in computer programming languages.

Arcsine function :- The arcsine is one of the inverse trigonometric functions (antitrigonometric functions) and is the inverse of the sine function. It is sometimes written as sin-1(x), but this notation should be avoided as it can be confused with an exponent notation (power of, raised to the power of). The arcsine is used to obtain an angle from the sine trigonometric ratio, which is the ratio between the side opposite to the angle and the longest side of the triangle.

The function spans from -1 to 1, and so do the results from our arcsin calculator. The range of the angle values is usually between -90° and 90°. There are a number of arcsin rules, like that sin(arcsin(x)) = x, or that arcsinα + arcsinβ = arcsin(α√(1-β2) + β√(1-α2)), as well as cosine of the arcsine: cos(arcsin(x)) = sin(arccos(x)) = √(1-x2), which can help you in trigonometry calculus.