Arcsin (Inverse Sine) Calculator

About Arcsin (Inverse Sine) Calculator

Welcome to the Arcsin (Inverse Sine) Calculator. Enter a sine value x (where −1 ≤ x ≤ 1) and get the corresponding principal angle θ₀ = arcsin(x) in degrees or radians. This tool also clarifies the principal value range (−90° to 90° / −π/2 to π/2) and shows the general solution for all angles that satisfy sin θ = x. Adjustable precision lets you format the output from 1 to 1000 decimal places. Precise results are powered by true arbitrary‑precision arithmetic.

Why this tool is different (USP)

• High precision up to 1000 decimal places — far beyond the 15–16 digits of common calculators.
• Arbitrary‑precision engine for stable and trustworthy scientific‑grade results.
• Clear principal value in degrees or radians, plus full general solutions.
• Unit circle visualization to build intuition about where solutions lie.
• Helpful validation for inputs outside the arcsin domain (−1 ≤ x ≤ 1).

What this calculator provides

• Principal value θ₀ = arcsin(x) with your chosen precision.
• Output in degrees or radians (your choice).
• Domain validation and clear error messages for |x| > 1.
• General solutions: θ = θ₀ + 2kπ or θ = (π − θ₀) + 2kπ.
• Educational, step‑by‑step explanation of the process.
• Ideal for trigonometry, geometry, physics, and engineering tasks.

Principal value range

By definition, arcsin returns the unique principal value θ₀ in the interval [−π/2, π/2] (i.e., [−90°, 90°]) such that sin(θ₀) = x. All other angles with the same sine value can be obtained from the general solution relationships described in the result section.