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  "page": "https://www.calculatorx.com/calc/math/arcsin",
  "api": "https://www.calculatorx.com/api/v1/calc/arcsin",
  "schema_input": "https://www.calculatorx.com/schemas/math.arcsin.input.json",
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  "assumptions": [
    "Real inverse sine with principal branch [−π/2, π/2] (NIST DLMF §4.23(ii)). Complex arcsin is not returned.",
    "Opposite/hypotenuse in the UI is a local triangle convenience (hypotenuse > 0, opposite ≥ 0, opposite ≤ hypotenuse). The published engine is arcsin(x). Use Decimal for a signed ratio, and Sin for the forward map.",
    "When x is exactly a listed common value (0, ±1/2, ±√2/2, ±√3/2, ±1), the engine returns the exact algebraic angle such as 30° = π/6. Nearby floats are not snapped."
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    "Non-numeric, object, array, boolean, NaN, or Infinity inputs return INVALID_NUMBER.",
    "x < −1 or x > 1 returns NOT_REAL (not clamped).",
    "arcsin(−1) = −90°; arcsin(0) = 0°; arcsin(0.5) = 30°; arcsin(1) = 90°."
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      "url": "https://dlmf.nist.gov/4",
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      "section": "Inverse trigonometric functions; principal values",
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