Calculate the arcsine (inverse sine) of a value and return the angle in degrees and radians with exact fractions of pi.
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Result
The angle whose sine equals 0.
Also in Functions
Trigonometry
The arcsin calculator finds the angle whose sine equals a given value. Enter any number between -1 and 1 to get the angle in both degrees and radians, with exact fractions of pi for common values.
Arcsine (sin⁻¹ or asin) is the inverse of the sine function. If sin(30°) = 0.5, then arcsin(0.5) = 30°. The result is always in the range -90° to 90° (or -pi/2 to pi/2 radians).
The domain of arcsine is [-1, 1] because the sine function only produces values in that range. Inputs outside this interval have no real solution.
θ = arcsin(x), where -1 ≤ x ≤ 1
Returns the angle θ in the range [-90°, 90°].
Arcsine returns only the principal value. Other angles with the same sine value (e.g. 150° also has sin = 0.5) are not shown. Use the supplementary angle rule: sin(180° - θ) = sin(θ).
Frequently asked questions
0 degrees (0 radians). sin(0°) = 0, so arcsin(0) = 0°.
Arcsin is the inverse function of sine: it returns an angle from a ratio. Cosecant (csc) is the reciprocal of sine: csc(x) = 1/sin(x). They are different operations.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Calculate the arccosine (inverse cosine) of a value and return the angle in degrees and radians with exact fractions of pi.
Calculate the arctangent (inverse tangent) of any real number and return the angle in degrees and radians.
Calculate the sine of an angle in degrees or radians with exact values for common angles like 30, 45, and 60 degrees.
Calculate the cosine of an angle in degrees or radians with exact values for common angles.
