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This PR enhances the trigonometric functions documentation and adds comprehensive examples of trigonometric laws with practical notebook implementations.

Documentation Enhancements

  • Cosine Law Extensions: Added documentation showing how the Cosine Law extends the Pythagorean theorem
  • Special Triangle Cases: Documented behavior for isosceles and equilateral triangles
  • Sine Law Comprehensive Coverage: Added alternative forms and complete documentation of the Sine Law
  • SSA Triangle Analysis: Documented Side-Side-Angle scenarios including impossible triangle cases

Practical Examples

  • Notebook Implementation: Added comprehensive worked examples in Basics.ipynb
  • Cosine Law Examples: SSS (Side-Side-Side) and SAS (Side-Angle-Side) scenarios
  • Sine Law Examples: AAS (Angle-Angle-Side) and SSA (Side-Side-Angle) scenarios
  • Error Handling: Demonstrated proper error handling for impossible triangle calculations
  • Educational Clarity: Clear explanations of when triangles are mathematically impossible

Technical Improvements

  • Julia Best Practices: Used try-catch blocks for graceful error handling in domain errors
  • Mathematical Accuracy: Proper handling of inverse trigonometric functions with domain restrictions
  • Symbol Usage: Updated copilot instructions for consistent mathematical symbol usage

Key Files Modified

  • docs/src/Trigonometry/02 Trigonometric Functions.md: Enhanced with comprehensive law documentation
  • notebooks/Basics.ipynb: Added practical examples with error handling
  • .github/copilot-instructions.md: Updated mathematical symbol guidelines

🎯 Educational Impact

  • Complete coverage of fundamental trigonometric laws
  • Practical examples with step-by-step calculations
  • Proper error handling demonstrations
  • Clear explanations of mathematical limitations
  • Enhanced learning experience with interactive notebook examples

This enhancement provides a comprehensive foundation for trigonometric studies with both theoretical documentation and practical computational examples.

 - Add to documentation how Cosine law is extension of Pythagorean function
 - Add example in notebook of two sides and an angle
 - Add to documentation alternative forms of the Sine Law
- Add to documenation of Cosine law information about isosceles triangles and equilateral triangles
 - Add examples in notebook of the Cosine Law
- alternate angle characters
- add general note about SSA cases.
- add Sine Law example
@AronT-TLV AronT-TLV merged commit 4b990c5 into main Sep 4, 2025
3 checks passed
@AronT-TLV AronT-TLV deleted the feature/trigonometric-studies branch September 5, 2025 14:14
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