How to Find Arcsin

Arcsin is a trigonometric function to lớn calculate the inverse sine. Arcsin can also be expressed as sin-1(x).

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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).


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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.

Table showing common sine values & inverse sine values for each in degrees & radians.

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SineAngle (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
00
√6 – √2 / 415°π / 12
1 / 230°π / 6
√2 / 245°π / 4
√3 / 260°π / 3
√6 + √2 / 475°5π / 12
190°π / 2

You might also be interested in our inverse cosine and inverse tangent calculators.