How to Find Arcsin
Arcsin is a trigonometric function to lớn calculate the inverse sine. Arcsin can also be expressed as sin-1(x).Bạn đang xem: Sine calculator
Arcsin is used to lớn undo or reverse the sine function. If you know the sine of an angle, you can use arcsin to lớn calculate the angle.
Since arcsin is the inverse of the sine function, & many angles nội dung 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 & is the angle in the range of -90° khổng lồ 90°.
To calculate arcsin, use a scientific calculator và 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 khổng lồ 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) khổng lồ (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 và ends at x = 1. Since the peak of the sine wave is at π / 2 radians và 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 & the arcsin, or angle for each of them.
| -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.