{
  "software": "apple-numbers",
  "function": "ACOS",
  "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/acos-ffa5c74880/15.4/web/1.0",
  "passed": 7,
  "total": 7,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B2))",
      "variables": {
        "B2": -1.0
      },
      "expected": 180.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B3))",
      "variables": {
        "B3": -0.866025403784439
      },
      "expected": 150.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B4))",
      "variables": {
        "B4": -0.5
      },
      "expected": 120.00000000000001,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B5))",
      "variables": {
        "B5": 0.0
      },
      "expected": 90.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B6))",
      "variables": {
        "B6": 0.5
      },
      "expected": 60.00000000000001,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B7))",
      "variables": {
        "B7": 0.707106781186548
      },
      "expected": 45.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B8))",
      "variables": {
        "B8": 1.0
      },
      "expected": 0.0,
      "numeric": true,
      "scope": "recovered worked example"
    }
  ],
  "independent_results": [
    {
      "case": 1,
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B2))",
      "actual_independent_model": 180.0,
      "expected": 180.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 2,
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B3))",
      "actual_independent_model": 150.00000000000006,
      "expected": 150.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 3,
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B4))",
      "actual_independent_model": 120.00000000000001,
      "expected": 120.00000000000001,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 4,
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B5))",
      "actual_independent_model": 90.0,
      "expected": 90.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 5,
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B6))",
      "actual_independent_model": 60.00000000000001,
      "expected": 60.00000000000001,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 6,
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B7))",
      "actual_independent_model": 44.999999999999964,
      "expected": 45.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 7,
      "software": "apple-numbers",
      "function": "ACOS",
      "expression": "=DEGREES(ACOS(B8))",
      "actual_independent_model": 0.0,
      "expected": 0.0,
      "passed": true,
      "scope": "recovered worked example"
    }
  ]
}