What is the domain of arcsin?

The domain of arcsin is [-1, 1]. You can only input values between -1 and 1 (inclusive). Values outside this range will result in an error or undefined result.

Why does arcsin(x) range from −90° to 90°?

Arcsin is defined to return values in the range [-90°, 90°] (or [-π/2, π/2] radians) to make it a function (one input gives one output). This is called the principal value range.

📐 Arcsin Calculator (Inverse Sine)

Find arcsin(x) and view angle outputs in degrees or radians.

Arcsin Calculator

Value(Domain: -1 ≤ x ≤ 1)

arcsin(x) =

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Arcsin, also written as sin⁻¹, is the inverse function of sine. Given a value between -1 and 1, arcsin returns the angle (in radians or degrees) whose sine equals that value. The range of arcsin is -90° to 90° (or -π/2 to π/2 radians).

Quick Examples

Common arcsin values you might encounter.

arcsin(0) = 0° or 0 rad

The angle whose sine is 0 is 0 degrees.

arcsin(0.5) = 30° or π/6 rad

The angle whose sine is 0.5 is 30 degrees.

arcsin(1) = 90° or π/2 rad

The angle whose sine is 1 is 90 degrees.

arcsin(-1) = -90° or -π/2 rad

The angle whose sine is -1 is -90 degrees.

Use Cases

Common applications of the arcsin function.

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Triangle Solving

Finding angles from side ratios
Solving inverse trigonometric problems
Calculating unknown angles

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Education

Understanding inverse functions
Learning trigonometric identities
Calculus applications

Frequently Asked Questions

Common questions about the arcsin function.

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Last updated: 2025-10-21 — Compiled and reviewed by Calvin (Math Research, FreeCalculators.app)