https://github.com/anar-bastanov/cosine-wave-polynomials

A console application that outputs multiple-angle formulas and trigonometric identities given the multiplier and a specific format.
https://github.com/anar-bastanov/cosine-wave-polynomials

c-sharp chebyshev-polynomial chebyshev-polynomials csharp formula-generation formula-generator math pascal-triangle polynomials python trigonometric-formulas trigonometry

Last synced: 26 days ago
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A console application that outputs multiple-angle formulas and trigonometric identities given the multiplier and a specific format.

• Host: GitHub
• URL: https://github.com/anar-bastanov/cosine-wave-polynomials
• Owner: anar-bastanov
• License: mit
• Created: 2024-08-10T19:23:43.000Z (3 months ago)
• Default Branch: main
• Last Pushed: 2024-08-16T18:04:41.000Z (3 months ago)
• Last Synced: 2024-09-30T12:21:21.025Z (about 1 month ago)
• Topics: c-sharp, chebyshev-polynomial, chebyshev-polynomials, csharp, formula-generation, formula-generator, math, pascal-triangle, polynomials, python, trigonometric-formulas, trigonometry
• Language: C#
• Homepage:
• Size: 13.7 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.txt

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README

        
# Cosine Wave Polynomials

A console application that outputs multiple-angle formulas and trigonometric identities given the multiplier and a specific format. This repository contains two functionally the same applications, one written in C# and the other in Python.

The algorithm generating desired polynomials uses one of two approaches to compute coefficients, famous Pascal's triangle and Chebyshev polynomials of the first kind.

## Examples

| Multiplier | Format | Output Formula |

|:----------:|:------:|:---------------|

| 2 | Cosine Only     | $`cos(2 * x)  =  - 1 + 2 cos(x)^2`$ |

| 2 | Sine And Cosine | $`cos(2 * x)  =  - sin(x)^2 + cos(x)^2`$ |

| 3 | Cosine Only     | $`cos(3 * x)  =  - 3 cos(x) + 4 cos(x)^3`$ |

| 3 | Sine And Cosine | $`cos(3 * x)  =  - 3 sin(x)^2 cos(x) + cos(x)^3`$ |

| 5 | Cosine Only     | $`cos(5 * x)  =  5 cos(x) - 20 cos(x)^3 + 16 cos(x)^5`$ |

| 5 | Sine And Cosine | $`cos(5 * x)  =  5 sin(x)^4 cos(x) - 10 sin(x)^2 cos(x)^3 + cos(x)^5`$ |

| 9 | Cosine Only     | $`cos(9 * x)  =  9 cos(x) - 120 cos(x)^3 + 432 cos(x)^5 - 576 cos(x)^7 + 256 cos(x)^9`$ |

| 9 | Sine And Cosine | $`cos(9 * x)  =  9 sin(x)^8 cos(x) - 84 sin(x)^6 cos(x)^3 + 126 sin(x)^4 cos(x)^5 - 36 sin(x)^2 cos(x)^7 + cos(x)^9`$ |

| ... |

The input multiplier has no theoretical limit; however, these formulas can become extremely lengthy due to their rapidly growing coefficients.

## References

* https://mathworld.wolfram.com/Multiple-AngleFormulas.html

* https://www.anirdesh.com/math/trig/cosine-identities.php

* https://en.wikipedia.org/wiki/Pascal%27s_triangle

* https://en.wikipedia.org/wiki/Chebyshev_polynomials

## License

Copyright © 2024 Anar Bastanov  

Distributed under the [MIT License](http://www.opensource.org/licenses/mit-license.php).