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ERIC Number: EJ1093394
Record Type: Journal
Publication Date: 2014
Pages: 8
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0819-4564
EISSN: N/A
Giving More Realistic Definitions of Trigonometric Ratios II
Bhattacharjee, Pramode Ranjan
Australian Senior Mathematics Journal, v28 n1 p57-64 2014
This paper being an extension of Bhattacharjee (2012) is very much relevant to Year 9 to Year 10A in the "Australian Curriculum: Mathematics". It also falls within the purview of class IX to class XII curriculum of Mathematics in India (Revised NCERT curriculum) for students aged 14-17 years. In Bhattacharjee (2012), the discovery of flaw in the traditional definitions of trigonometric ratios, which make use of the most unrealistic concept of negative length or distance has been reported. With a view to getting rid of such unrealistic concept of negative length or distance, which has been in regular use in the sign convention of geometrical optics, in solving typical problems of elementary mechanics, efforts have already been made by the author earlier in Bhattacharjee (2002, 2011, 2012). To uproot the misleading concept of negative length or distance from the basic level of trigonometry, realistic definitions of trigonometric ratios have been offered in Bhattacharjee (2012) with the help of vector algebra and they have been subsequently employed to derive the basic formulae of trigonometry in an unambiguous manner. Such a vectorial portrayal of realistic definitions of trigonometric ratios offered in Bhattacharjee (2012) had been much clearer leaving no room for confusion. Now, with the development of the realistic definitions of trigonometric ratios in Bhattacharjee (2012), there is an urgent need how they lead to other useful formulae of trigonometry. With that point in mind, the realistic definitions of trigonometric ratios offered in Bhattacharjee (2012) have been applied in this paper to derive some of the other useful formulae of trigonometry. The study reveals that the application of the realistic definitions of trigonometric ratios offered in Bhattacharjee (2012) leads directly to those useful formulae of trigonometry. The approach, in all cases considered, is novel, analytical and straight forward unlike the well known geometrical or vectorial approaches found in the traditional literature, Hall and Knight (1906), Spiegel (1959). As a result, the present work will not only enrich the relevant branch of mathematics but it will also enhance the same as well.
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: Secondary Education
Audience: N/A
Language: English