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Free arcsin calculator & inverse sine calculator. Calculate arcsin, sin⁻¹, and arcsine values in radians and degrees with detailed analysis. Our calculator uses inverse trigonometric functions to determine the angle whose sine equals your input value, with support for principal values and general solutions.
Last updated: February 2, 2026
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Enter a value between -1 and 1 (sine range)
Principal Value:
0.523599 rad
Radians:
0.523599 rad
Degrees:
30.0000°
Verification:
sin(0.523599 rad) = 0.5
General Solution:
θ = 0.5236 + 2πn OR θ = 2.6180 + 2πn (where n is any integer)
Analysis:
arcsin(0.5) = π/6 ≈ 0.5236 rad (30°): Common trigonometric value
Arcsin Properties:
Function notation
arcsin(x) = sin⁻¹(x)
Returns the angle whose sine is x, where x ∈ [-1, 1]
Range in radians
[-π/2, π/2]
Principal values from approximately -1.5708 to 1.5708 radians
Range in degrees
[-90°, 90°]
Principal values from -90 degrees to 90 degrees
Equivalent notations
arcsin = arcsine = sin⁻¹
All three notations represent the same inverse function
Notation meaning
sin⁻¹(x) ≠ 1/sin(x)
The -1 represents inverse function, not reciprocal
Valid domain
-1 ≤ x ≤ 1
Only accepts values that sine function can produce
For arcsin(0.5) - finding the angle whose sine is 0.5:
In Radians
π/6 ≈ 0.5236
In Degrees
30°
Our arcsin calculator uses the inverse sine function to determine the angle whose sine equals your input value. The calculator applies mathematical principles of inverse trigonometric functions to provide accurate results in both radians and degrees.
If sin(θ) = x, then arcsin(x) = θDomain: -1 ≤ x ≤ 1Range: -π/2 ≤ θ ≤ π/2 (radians)Range: -90° ≤ θ ≤ 90° (degrees)The arcsin function is the inverse of sine restricted to the domain [-π/2, π/2]. This restriction ensures that arcsin is a proper function with exactly one output for each valid input.
Shows arcsin values on the unit circle in the right half
The arcsin function is one of the fundamental inverse trigonometric functions. It undoes the sine operation, taking a ratio and returning the corresponding angle. The principal value is restricted to [-π/2, π/2] to ensure the function is well-defined and one-to-one.
Need help with other trigonometry? Check out our inverse tangent calculator and law of cosines calculator.
Get Custom Calculator for Your PlatformResult: arcsin(√3/2) = π/3 ≈ 1.0472 radians = 60°
This is a common trigonometric value corresponding to a 60° angle.
arcsin(1/2) = ?
π/6 = 30° (special angle)
arcsin(-√2/2) = ?
-π/4 = -45° (fourth quadrant)
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