{
  "software": "apple-numbers",
  "function": "ACOT",
  "native_application_execution": false,
  "checked_date": "2026-10-12",
  "method": "Independent mathematical/text-processing models, not Apple Numbers or Zoho Sheet execution; random tests check documented bounds/transforms, not randomness.",
  "official_function_reference": "https://support.apple.com/guide/functions/acot-f4239ce6f1/15.4/web/1.0",
  "passed": 8,
  "total": 8,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B2)",
      "variables": {
        "B2": -5
      },
      "expected": 2.9441970937399127,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B3)",
      "variables": {
        "B3": -2
      },
      "expected": 2.677945044588987,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B4)",
      "variables": {
        "B4": -1
      },
      "expected": 2.356194490192345,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B5)",
      "variables": {
        "B5": 0
      },
      "expected": 1.5707963267948966,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B6)",
      "variables": {
        "B6": 0.5
      },
      "expected": 1.1071487177940904,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B7)",
      "variables": {
        "B7": 1
      },
      "expected": 0.7853981633974483,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B8)",
      "variables": {
        "B8": 2
      },
      "expected": 0.46364760900080615,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B9)",
      "variables": {
        "B9": 5
      },
      "expected": 0.19739555984988066,
      "numeric": true,
      "scope": "recovered worked example"
    }
  ],
  "independent_results": [
    {
      "case": 15,
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B2)",
      "actual_independent_model": 2.9441970937399127,
      "expected": 2.9441970937399127,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 16,
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B3)",
      "actual_independent_model": 2.677945044588987,
      "expected": 2.677945044588987,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 17,
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B4)",
      "actual_independent_model": 2.356194490192345,
      "expected": 2.356194490192345,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 18,
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B5)",
      "actual_independent_model": 1.5707963267948966,
      "expected": 1.5707963267948966,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 19,
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B6)",
      "actual_independent_model": 1.1071487177940904,
      "expected": 1.1071487177940904,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 20,
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B7)",
      "actual_independent_model": 0.7853981633974483,
      "expected": 0.7853981633974483,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 21,
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B8)",
      "actual_independent_model": 0.46364760900080615,
      "expected": 0.46364760900080615,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 22,
      "software": "apple-numbers",
      "function": "ACOT",
      "expression": "=ACOT(B9)",
      "actual_independent_model": 0.19739555984988066,
      "expected": 0.19739555984988066,
      "passed": true,
      "scope": "recovered worked example"
    }
  ]
}