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.