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ERIC Number: EJ992376
Record Type: Journal
Publication Date: 2012
Pages: 7
Abstractor: ERIC
Reference Count: 16
ISBN: N/A
ISSN: ISSN-0819-4564
Giving More Realistic Definitions of Trigonometric Ratios
Bhattacharjee, Pramode Ranjan
Australian Senior Mathematics Journal, v26 n2 p21-27 2012
Trigonometry is a well known branch of Mathematics. The study of trigonometry is of great importance in surveying, astronomy, navigation, engineering, and in different branches of science. This paper reports on the discovery of flaws in the traditional definitions of trigonometric ratios of an angle, which (in most cases) make use of the most unrealistic concept of negative length (or distance). With a view to getting rid of the misleading concept of negative length (distance), the definitions of novel trigonometric ratios (falling within the purview of Year 9 to Year 10A in the "Australian Curriculum: Mathematics") have been offered first with the help of vector algebra and then subsequently employed to derive some important formulae of trigonometry. This paper first considers the traditional branch of trigonometry, examines it to see that it is very much unrealistic at its root level and finally it gives birth to the definitions of novel trigonometric ratios of an angle with the help of vector algebra so as to uproot the most unrealistic concept of negative length. It deals with a debatable issue regarding the misleading concept of negative length (distance) prevailing at the basic level of defining trigonometric ratios of an angle in the traditional literature and in fact reflects a discovery of real truth. (Contains 3 figures.)
Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Australia