{
 "id": "source/mactutor-trigonometric-functions",
 "class": "source",
 "slug": "mactutor-trigonometric-functions",
 "label": {
  "ar": "تاريخ الدوال المثلثية — ماكتوتر",
  "en": "The trigonometric functions — MacTutor",
  "ur": "مثلثی تفاعلات کی تاریخ — میک ٹیوٹر"
 },
 "summary": {
  "ar": "تاريخ عام يميز طريق الأوتار والجيوب من طريق الظلال وتاريخ الألفاظ اللاحق.",
  "en": "General history separating chord/sine and shadow routes and later naming conventions.",
  "ur": "عمومی تاریخ جو وتر و جیب اور سائے کے راستے اور بعد کے نام الگ رکھتی ہے۔"
 },
 "stub": false,
 "wings": [],
 "regions": [],
 "periods": [],
 "tags": [],
 "aliases": [],
 "themes": [],
 "data": {
  "kind": "secondary",
  "type": "webpage",
  "title": "The trigonometric functions",
  "author": [
   {
    "family": "O'Connor",
    "given": "J J"
   },
   {
    "family": "Robertson",
    "given": "E F"
   }
  ],
  "issued": {
   "date-parts": [
    [
     1996,
     6
    ]
   ]
  },
  "publisher": "MacTutor History of Mathematics, University of St Andrews",
  "language": "en",
  "URL": "https://mathshistory.st-andrews.ac.uk/HistTopics/Trigonometric_functions/",
  "open_access": true,
  "reliability_note": "Complete actual history/byline/update read. General circa860 Arabic shadow-table statement not an exact Habash composition date or separate individual identity proof. Umbra recta/versa, later tangent/cotangent names distinguished from modern elevation convention. No malformed web-rendered formula copied; modern teaching arithmetic independently checked.",
  "status": {
   "review": "published",
   "completeness": 3,
   "generated_by": "Copilot SDK in VS Code"
  },
  "provenance": {
   "generated_by": "Copilot SDK in VS Code",
   "model": "unknown",
   "run": "inventions-p3-b57",
   "source": "Actual complete authored MacTutor history; contextual source, not a transcription of Habash."
  }
 },
 "prose": {},
 "degree": 0,
 "contemporaries": [],
 "updated": "2026-11-06",
 "connections": [],
 "related": [],
 "license": {
  "prose": "CC BY-SA 4.0",
  "data": "CC0 1.0"
 }
}