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  "api": "https://www.calculatorx.com/api/v1/calc/arccos",
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  "schema_output": "https://www.calculatorx.com/schemas/math.arccos.output.json",
  "assumptions": [
    "Real inverse cosine with principal branch [0, π] (NIST DLMF §4.23(ii)). Complex arccos is not returned.",
    "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 60° = π/3. Nearby floats are not snapped."
  ],
  "limitations": [
    "x outside [−1, 1] → NOT_REAL",
    "Missing x → MISSING_REQUIRED_INPUT",
    "Near-common-value hint is display metadata; it does not replace the canonical deg/rad or assert mathematical exactness.",
    "Raw input accepts finite JSON numbers or decimal strings; normalized inputs contain numeric x only. Nonzero text rounded to zero is NUMERIC_UNDERFLOW.",
    "Unknown inputs are UNKNOWN_INPUT; x/xInput conflicts are AMBIGUOUS_INPUT.",
    "Legacy engine test counts are separate from the CVP Manifest suite. CVP identity is included; production status requires the linked report matched by version, revision and digest."
  ],
  "boundary_conditions": [
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    "REST/MCP accept only x and xInput; unknown fields return UNKNOWN_INPUT and conflicting aliases return AMBIGUOUS_INPUT.",
    "Missing x returns MISSING_REQUIRED_INPUT.",
    "Non-numeric, object, array, boolean, NaN, or Infinity inputs return INVALID_NUMBER.",
    "x < −1 or x > 1 returns NOT_REAL. Direct user input is not clamped onto the domain, even if |x| − 1 is only a few 1e-13.",
    "arccos(1) = 0°; arccos(0.5) = 60°; arccos(0) = 90°; arccos(−1) = 180°."
  ],
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      "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",
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    },
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      "title": "NIST DLMF §4.23",
      "section": "Inverse trigonometric functions; principal values",
      "url": "https://dlmf.nist.gov/4.23",
      "supports": "Principal arccos on [−1, 1] with range [0, π]; degree output is θ × 180/π",
      "kind": "reference",
      "publisher": "National Institute of Standards and Technology"
    },
    {
      "title": "CalculatorX mathematical conventions",
      "section": "Principal branch; exact algebraic values only for exact inputs",
      "supports": "Published engine is arccos(x). Direct inputs outside [−1, 1] are NOT_REAL with no domain clamp.",
      "kind": "definition"
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      "golden": 5,
      "boundary": 5,
      "property": 0
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}