Arcsin Calculator (Inverse Sine)

sin^-1() =

Degrees:

–

Radians:

–

π radians:

–

Graph of inverse sine

The domain is -1 ≤ x ≤ 1.

The range is -π/2 ≤ y ≤ π/2.

With this calculator, you can find the inverse sine result of any input value. The result will be displayed in degrees, radians and π radians, only considering the range -π/2 ≤ y ≤ π/2.

You can learn more about using the calculator below. Also, you can learn about the definition of inverse sine, its graph, and some important values.

How to use the inverse sine calculator?

Step 1: Enter the value of x in the first input box. The entered value must be in the domain -1 ≤ x ≤ 1.

Step 2: The angle in degrees will be displayed on the right side.

Step 3: Additional solutions in radians and π radians will be shown at the bottom.

What is the difference between degrees, radians, and π radians?

We can find the equivalence between degrees and radians by considering that a full circle has 360° and 2π radians. Therefore, we can deduce that 180° is equal to π radians.

On the other hand, the only difference between π radians and radians is that in “radians” the value has already been multiplied by π, while in “π radians” it has not. For example, the result 1.5 π radians is equal to 4.712, since π has a value of approximately 3.1415…

What is inverse sine?

The inverse sine, also called the arc sine, is the inverse function of the sine. The inverse sine function reverses the effects of the sine function. This function is denoted sin^-1(x) or also arcsin(x).

The output values of the sine function are equal to the input values of the inverse sine and vice versa. For example, the sine of 30° is equal to 0.5. This means that the inverse sine of 0.5 is equal to 30°.

We can use this function to determine the value of an angle if we have the proportions of the sides of a triangle. For example, we can find angle A in the following triangle using arcsin(x), where x equals a/c.

Why does the inverse sine function only accept values from -1 to 1?

The domain of the inverse sine function is from -1 to 1 because it is the inverse of the sine function. Therefore, the values of x and y are swapped.

Therefore, since there is no angle that we can use to get a sine value greater than 1 or less than -1, we also cannot use values of x outside of that range in the arcsine function.

Inverse sine graph

We can graph the arcsine function by considering specific intervals for the input and output values. In this calculator, we use x values from -1 to 1. This results in y values from -π/2 to π/2.

Inverse sine domain

From the graph, we can deduce that the domain of the arcsine function covers the values from -1 to 1. Therefore, the domain is -1 ≤ x ≤ 1.

Inverse sine range

Using the graph, we can deduce that the arcsine function has y-values ranging from -π/2 to π/2. Therefore, its range is -π/2 ≤ y ≤ π/2.

Table of inverse sines of common values

Value of x	arcsin(x)(rad)	arcsin(x)(°)
-1	-π/2	-90°
-√3/2	-π/3	-60°
-√2/2	-π/4	-45°
-1/2	-π/6	-30°
0	0	0°
1/2	π/6	30°
√2/2	π/4	45°
√3/2	π/3	60°
1	π/2	90°

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