{
  "software": "apple-numbers",
  "function": "ATAN2",
  "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/atan2-ffa5cb9325/15.4/web/1.0",
  "passed": 9,
  "total": 9,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B2,C2))",
      "variables": {
        "B2": 1,
        "C2": 0
      },
      "expected": 0.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B3,C3))",
      "variables": {
        "B3": 1,
        "C3": 1
      },
      "expected": 45.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B4,C4))",
      "variables": {
        "B4": 0,
        "C4": 1
      },
      "expected": 90.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B5,C5))",
      "variables": {
        "B5": -1,
        "C5": 1
      },
      "expected": 135.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B6,C6))",
      "variables": {
        "B6": -1,
        "C6": -1
      },
      "expected": -135.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B7,C7))",
      "variables": {
        "B7": 0,
        "C7": -1
      },
      "expected": -90.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B8,C8))",
      "variables": {
        "B8": 1,
        "C8": -1
      },
      "expected": -45.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B9,C9))",
      "variables": {
        "B9": 3,
        "C9": 4
      },
      "expected": 53.13010235415598,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B10,C10))",
      "variables": {
        "B10": -3,
        "C10": 4
      },
      "expected": 126.86989764584402,
      "numeric": true,
      "scope": "recovered worked example"
    }
  ],
  "independent_results": [
    {
      "case": 53,
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B2,C2))",
      "actual_independent_model": 0.0,
      "expected": 0.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 54,
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B3,C3))",
      "actual_independent_model": 45.0,
      "expected": 45.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 55,
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B4,C4))",
      "actual_independent_model": 90.0,
      "expected": 90.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 56,
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B5,C5))",
      "actual_independent_model": 135.0,
      "expected": 135.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 57,
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B6,C6))",
      "actual_independent_model": -135.0,
      "expected": -135.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 58,
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B7,C7))",
      "actual_independent_model": -90.0,
      "expected": -90.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 59,
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B8,C8))",
      "actual_independent_model": -45.0,
      "expected": -45.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 60,
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B9,C9))",
      "actual_independent_model": 53.13010235415598,
      "expected": 53.13010235415598,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 61,
      "software": "apple-numbers",
      "function": "ATAN2",
      "expression": "=DEGREES(ATAN2(B10,C10))",
      "actual_independent_model": 126.86989764584402,
      "expected": 126.86989764584402,
      "passed": true,
      "scope": "recovered worked example"
    }
  ]
}