{
  "capability_id": "math.arccos",
  "tool_id": "arccos",
  "engine": "arccos",
  "calculation_version": "1.0.6",
  "generated_at": "2026-10-15T08:30:11.022Z",
  "engine_build": "2026-10-15",
  "test_count": 10,
  "passed": 10,
  "failed": 0,
  "tests_summary": {
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      "total": 5,
      "passed": 5
    },
    "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": [
      "formula",
      "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/arccos",
  "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": [
    "Decimal strings are accepted and normalized to binary64 x. Nonzero decimal text that rounds to zero returns NUMERIC_UNDERFLOW; explicit zero remains valid.",
    "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°."
  ],
  "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 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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  "methods": [],
  "fingerprint": "sha256:e4934d43b5d94755afcbc9c5121de55f4cb8ca0159bb912f3c04fe59324f9219",
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      "expect": {
        "deg": 60
      },
      "expectWarning": null,
      "actual": {
        "deg": 60,
        "rad": 1.0471975511965976,
        "verification": {
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          "passed": true
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      "error": "Provide x or its alias xInput."
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