Arcsin (sin⁻¹) Calculator

Arcsin – Quick Cheat Sheet

Definition: θ = arcsin(x) gives the angle whose sine is x.
Domain: x ∈ [−1, 1]. Range (principal): θ ∈ [−90°, 90°] or [−π/2, π/2].
Common values: sin(0)=0 → arcsin(0)=0°; sin(1/2)=0.5 → 30°; sin(√2/2)≈0.7071 → 45°; sin(√3/2)≈0.8660 → 60°; sin(1)=1 → 90°.
All solutions for sin(θ)=x (degrees): θ = arcsin(x) + 360°·k or θ = (180° − arcsin(x)) + 360°·k.
All solutions (radians): θ = arcsin(x) + 2π·k or θ = (π − arcsin(x)) + 2π·k.
Conversions: radians ↔ degrees with deg = rad × 180/π, rad = deg × π/180.
Display rounding: numbers shown are rounded for readability; internal math uses full PHP precision.

Edge cases & notes

If |x| > 1, arcsin is undefined (domain error).
For x = 1 or x = −1, there is only one distinct base angle in [0°, 360°).
Angles shown under “base solutions” are normalized to their principal cycle: [0°,360°) or [0,2π).