Extended Angle Sum and Difference Identity Rules for Scalene Triangles

Luis Teia

Journal of Mathematics Research, 2022, vol. 14, issue 5, 21

Abstract: The present article extends the applicability of the angle sum and difference identity rules sin(A±B) and cos(A±B) beyond the particular case of a right-angled triangle into the general case of scalene triangles as sin*(A±B,γ) and cos*(A±B,γ), adding the effect of independently varying both the reference angle α = A±B and the obtuse angle γ. Accompanied by appropriate theorems and proofs, the mathematical end result are four updated equations that supersede the traditional expressions sin(A±B) = sin(A)cos(b)± cos(A)sin(B) and cos(A±B) = cos(α)cos(B) ∓ sin(A) sin(B), where the conventional sin(α) and cos(α) functions are replaced by the [already proven] extended versions sin*(α,γ) and cos*(α,γ) enclosing modifications including two angles α and γ. An open-source program scripted in Octave is provided for the verification of the derived expressions, including plotting the geometric results as a figure for both the cases of angle summation and subtraction.

Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://ccsenet.org/journal/index.php/jmr/article/download/0/0/47801/51461 (application/pdf)
https://ccsenet.org/journal/index.php/jmr/article/view/0/47801 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:14:y:2022:i:5:p:21

Access Statistics for this article

More articles in Journal of Mathematics Research from Canadian Center of Science and Education Contact information at EDIRC.
Bibliographic data for series maintained by Canadian Center of Science and Education ().