Ikuemuya’s Formula III: An Alternative Formula to the Law of Cosines for The Computation of Magnitude of Resultant Vector

O.E. Ikuemuya¹

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.3 , pp.31-34, Jun-2022

Online published on Jun 30, 2022

Copyright © O.E. Ikuemuya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This paper presents a simple formula for the use in Mathematics, Physics and Engineering in solving geometry related problems. It is a simple alternative formula to the law of cosines for use in the computation of magnitude of resultant vector in geometry. The formula is named the Ikuemuya’s formula III. It is simple and less cumbersome than the usual law of cosines and it does not involve the finding of squares and square roots of numbers when used in the computation of magnitude of resultant vectors as common with the law of cosines, it only makes use of basic arithmetic operation like addition, subtraction and multiplication, and the magnitude of the resultant vector can be computed quite easily.

Key-Words / Index Term :
Alternative formula, Average constant factor, Ikuemuya’s formula III, Law of cosines, Magnitude of resultant vector, Non-perfect squares.

References :
[1] CK-12 flexbook, “Resultant as magnitude and direction”, chap. 5, 2016
[2] Lawrence S. Leff, Barron’s Educational series, pp.326, 2005.
[3] Kevin K. Ferland, “Extending two classic proofs of the Pythagorean theorem to the law of cosines”, JSTOR, published by Taylor&Francis, Ltd. Vol 90, No 3 pp.182-186, 2017.
[4] Fl01000126.schoolwires.net, “Additional Topic in Trigonometry”, chapter 6, section 2, pp.657
[5] Jarno Mielikainen, “A novel full-search vector quantization algorithm based on the law of cosines”, IEEE signal processing letters 9 (6), 175-176, 2002.
[6] RB Kershner, “The law of sines and law of cosines for polygons”, mathematics magazines 44 (3), 150-153, 1971.
[7] M. W Anyakoha, New school Physics for senior secondary schools, pp. 113, 2010 edition.
[8] O.E Ikuemuya, “Accessible formulas for computing the magnitude of Resultant vector in 2 and 3-Dimensions”, International journal of scientific Research in mathematical and statistical sciences, Vol 9, issue 1, pp. 7-13, 2022.