Inverse Sine (asin) Calculator
Enter a value between -1 and 1 to find its arcsine.
What is arcsin?
The arcsine, written as arcsin(x) or sin-1(x), is the inverse of the sine function. It answers this question: “What angle has sine equal to x?”
For example, if sin(30°) = 0.5, then arcsin(0.5) = 30° (or π/6 radians).
Key domain and range rules
Domain (allowed input x)
Because sine values always stay between -1 and 1, the input to arcsin must satisfy:
-1 ≤ x ≤ 1
Range (output angle)
The principal output range of arcsin is:
[-π/2, π/2] radians OR [-90°, 90°]
Your calculator result is always returned in this principal range.
How this arcsin calculator works
- Step 1: Enter x between -1 and 1.
- Step 2: Choose radians or degrees.
- Step 3: Pick decimal precision.
- Step 4: Click Calculate arcsin(x).
Internally, the calculation uses JavaScript’s Math.asin(x), which returns radians.
If you choose degrees, the result is converted using:
degrees = radians × (180 / π)
Common arcsin values
- arcsin(-1) = -π/2 = -90°
- arcsin(-0.5) = -π/6 = -30°
- arcsin(0) = 0
- arcsin(0.5) = π/6 = 30°
- arcsin(1) = π/2 = 90°
Why inverse trig functions matter
Arcsin appears in geometry, physics, engineering, graphics, and signal processing. Anytime you know a ratio and need an angle, inverse trig is useful.
Typical use cases
- Finding an angle in a right triangle from opposite/hypotenuse.
- Motion analysis and oscillation problems.
- Computer graphics rotations and direction calculations.
- Control systems and wave analysis.
Frequent mistakes to avoid
- Using inputs outside [-1, 1]: arcsin is undefined there for real numbers.
- Mixing radians and degrees: always confirm your expected unit.
- Confusing arcsin with 1/sin: sin-1(x) means inverse sine, not reciprocal.
- Ignoring principal value: arcsin returns the principal angle only.
Quick FAQ
Is arcsin the same as csc?
No. arcsin is inverse sine. csc is the reciprocal trig function, 1/sin.
Can arcsin return multiple angles?
The equation sin(θ) = x has infinitely many solutions, but arcsin(x) returns one principal value in [-π/2, π/2].
Why does my calculator show NaN sometimes?
That usually happens when x is outside the valid domain or not entered as a number.
Final note
Use this tool for fast, reliable inverse sine calculations with unit conversion and precision control. If you work with trigonometry regularly, bookmark this page and use the quick-value buttons for instant checks.