[ARTICLE] Applied Physics of Extended (or Gamma) Sine and Cosine Functions (Canadian Journal of Applied Physics Research / 2023)
Creators: name: Teia, Luis
Publisher: name: figshare
Year: 2023
Subjects: classificationCode: 519999
subject: Other physical sciences not elsewhere classified
classificationCode: 510399
subject: Classical physics not elsewhere classified
classificationCode: 510906
subject: Space instrumentation
classificationCode: 400107
subject: Satellite, space vehicle and missile design and testing
classificationCode: 400199
subject: Aerospace engineering not elsewhere classified
classificationCode: 400504
subject: Construction engineering
classificationCode: 490204
subject: Mathematical aspects of general relativity
classificationCode: 490203
subject: Mathematical aspects of classical mechanics, quantum mechanics and quantum information theory
classificationCode: 490199
subject: Applied mathematics not elsewhere classified
classificationCode: 490499
subject: Pure mathematics not elsewhere classified
classificationCode: 490299
subject: Mathematical physics not elsewhere classified
classificationCode: 401001
subject: Engineering design
classificationCode: 401002
subject: Engineering education
classificationCode: 400913
subject: Radio frequency engineering

description: Evolution of fundamental mathematical tools (such as trigonometric functions sin(α) and cos(α)) has inherent repercusions on how we solve problems in applied physics. Recently published (see links below) extended or gamma sine function sin∗(α, γ) and cosine function cos∗(α, γ) — along with their upgraded identity angle sum and subtraction rules sin∗(A ± B, γ) and cos∗(A ± B, γ) — have enabled a new approach on how to tackle practical problems using mathematics (a published example is the energy-coupled mass-spring oscilatory system). The usefullness of a theory is measured by both the insight it generates, and the solution it produces, when applied to physical problems with pertinent applications. Its acceptance amongst peers depends on the availability of such examples, as way-showers of how the theory can be applied in practice, and how useful results can be derived by employing it in similar or related examples/problems. This article has the purpose of providing this bridge between the above theories and its application in some common scientific fields. Several exercises are solved employing these new formulae, and new potential applications are identified that cover various topics in physics such as civil engineering (i.e., measuring distances in bridges), aerospace and aeronautics (i.e., turbine velocity triangles and optimum orbital deployment for a satellite constellation) and telecommunications (i.e., antenna array beamforming and steering, as well as new modulations based on quadrature phase-shift keying). These problems (and solutions) are designed to indicate the usefullness of these new expanded functions, and can become practical classroom exercises applicable to both academic and professional environments.APR link: Applied Physics of Extended (or Gamma) Sine and Cosine FunctionsJMR link #1: Extended Angle Sum and Difference Identity Rules for Scalene TrianglesJMR link #2: Extended Sine and Cosine Functions for Scalene Triangles<b>Copyrights</b>Copyright for this article is retained by the author(s), with first publication rights granted to the journal. This is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).-------------------------------------------------------------------------For more public data, please visit my Figshare profile: https://figshare.com/authors/Luis_Teia/10811244