{
  "capability_id": "math.arcsin",
  "tool_id": "arcsin",
  "engine": "arcsin",
  "calculation_version": "1.0.6",
  "generated_at": "2026-10-13T07:09:36.761Z",
  "engine_build": "2026-10-12",
  "test_count": 11,
  "passed": 11,
  "failed": 0,
  "tests_summary": {
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      "total": 6,
      "passed": 6
    },
    "boundary": {
      "total": 5,
      "passed": 5
    },
    "property": {
      "total": 0,
      "passed": 0
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  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
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      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
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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",
  "schema_output": "https://www.calculatorx.com/schemas/math.arcsin.output.json",
  "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."
  ],
  "limitations": [
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    "Missing x → MISSING_REQUIRED_INPUT"
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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°."
  ],
  "sources": [
    {
      "title": "NIST Digital Library of Mathematical Functions, Chapter 4",
      "section": "Elementary Functions",
      "url": "https://dlmf.nist.gov/4",
      "supports": "Inverse trigonometric functions as elementary inverses of sine, cosine, and tangent",
      "kind": "reference"
    },
    {
      "title": "NIST DLMF §4.23",
      "section": "Inverse trigonometric functions; principal values",
      "url": "https://dlmf.nist.gov/4.23",
      "supports": "Principal arcsin on [−1, 1] with range [−π/2, π/2]; degree output is θ × 180/π",
      "kind": "reference"
    },
    {
      "title": "CalculatorX mathematical conventions",
      "section": "Principal branch; exact-value recognition; triangle mode is UI-only",
      "supports": "Published engine is arcsin(x). Opposite/hypotenuse is a local triangle convenience (positive sides, opposite ≤ hypotenuse). Inputs outside [−1, 1] are NOT_REAL.",
      "kind": "definition"
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  ],
  "methods": [],
  "fingerprint": "sha256:8b0ca85172bad3c38d04c345763988b44c0da613b05f655d338463c21b388f1d",
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      "ok": true,
      "kind": "golden",
      "inputs": {
        "x": 0.5
      },
      "expect": {
        "deg": 30,
        "rad": 0.5235987755982988
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      "expectWarning": null,
      "actual": {
        "deg": 30,
        "rad": 0.5235987755982988,
        "verification": {
          "expression": "sin(result)",
          "value": 0.49999999999999994,
          "passed": true
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        "exact": true
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      "tol": 1e-12
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          "passed": true
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