Inverse Sine Calculator – Calculate arcsin(x)
Find the angle in degrees or radians using the inverse sine with the arcsin calculator below.
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How to Find Arcsin
Arcsin is a trigonometric function to calculate the inverse sine. Arcsin can also be expressed as sin-1(x).
Arcsin is used to undo or reverse the sine function. If you know the sine of an angle, you can use arcsin to calculate the angle.
Since arcsin is the inverse of the sine function, and many angles share the same sine value, arcsin is a periodic function. Each arcsin value can result in multiple angle values. The primary result for arcsin is known as the principal value and is the angle in the range of -90° to 90°.
To calculate arcsin, use a scientific calculator and the asin function, or just use the calculator above. Most scientific calculators require the angle value in radians to solve for sin.
Inverse Sine Formula
The inverse sine formula is:
y = sin(x) | x = arcsin(y)
Thus, if y is equal to the sine of x, then x is equal to the arcsin of y.
Inverse Sine Graph
If you graph the arcsin function for every possible value of sine, it forms a curve from (-1, –π / 2) to (1, π / 2).
Because the value of sine is always in the range of -1 to 1, the inverse sine curve starts at x = -1 and ends at x = 1. Since the peak of the sine wave is at π / 2 radians and the dip of the wave is at –π / 2 radians, the y value ends at those points.
Inverse Sine Table
The table below shows common sine values and the arcsin, or angle for each of them.
| Sine | Angle (degrees) | Angle (radians) |
|---|---|---|
| -1 | -90° | –π / 2 |
| –√6 + √2 / 4 | -75° | –5π / 12 |
| –√3 / 2 | -60° | –π / 3 |
| –√2 / 2 | -45° | –π / 4 |
| –1 / 2 | -30° | –π / 6 |
| –√6 – √2 / 4 | -15° | –π / 12 |
| 0 | 0° | 0 |
| √6 – √2 / 4 | 15° | π / 12 |
| 1 / 2 | 30° | π / 6 |
| √2 / 2 | 45° | π / 4 |
| √3 / 2 | 60° | π / 3 |
| √6 + √2 / 4 | 75° | 5π / 12 |
| 1 | 90° | π / 2 |
You might also be interested in our inverse cosine and inverse tangent calculators.