ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC

S. Ekmekçi; Z. Akça; K. Altıntaş

doi:10.36753/mathenot.421326

EN

ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC

Abstract

In this paper, the plane with the generalized taxicab metric is

considered and the trigonometric functions and the norm are dened. Then,

the cosine and the sine functions are developed by using the reference angle

with respect to the generalized taxicab metric. It is shown that Schwarz's

inequality is valid under restricted case of d_Tg -metric. Finally, the area of

any triangle in the plane with the generalized taxicab metric is given as the

geometrical interpretation that contains the trigonometric functions and norm.

Keywords

trigonometric functions,non- Euclidean metric,generalized taxicab metric

References

[1] Akça, Z., Bayar, A. and Ekmekçi, S., The norm in CC-plane geometry. Pi Mu Epsilon J. 12 (2007), no. 6, 321-324 .
[2] Akça, Z. and Kaya, R., On Taxicab Trigonometry. Jour. of Inst. of Math & Comp. Sci. (Math. Ser.) 10 (1997), no. 3, 151-159 .
[3] Altıntaş, A.K., Oklidyen Düzlemdeki Bazı Geometrik Problemlerin Genelleştirilmiş Taksi Metrikli Geometriye Uygulaması. Eskişehir Osmangazi Universitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 2009.
[4] Bayar, A., On Trigonometric Functions in Maximum Metric. Kog 12 (2008), 45-48 .
[5] Bayar, A. , Ekmekçi, S., Özcan, M., On Trigonometric Functions and Cosine and Sine Rules in Taxicab Plane. International Electronic Journal Of Geometry 2 (2009), no. 1, 17-24 .
[6] Bayar, A., Ekmekçi, S. and Akça, Z., On the plane geometry with generalized absolute value metric. Mathematical Problems in Engineering Vol.2008, Article ID 673275, 8 pages.
[7] Bayar, A. and Ekmekçi, S., On the Chinese-Checker Sine And Cosine Functions. International Journal of Mathematics and Analysis 1 (2006), no. 3, 249-259 .
[8] Brisbin, R. and Artola, P., Taxicab Trigonometry. Pi Mu Epsilon J. 8 (1985), no. 2, 89-95 .
[9] Ekmekçi, S., Bayar, A., Altıntaş, A. K., On the Group of Isometries of the Generalized Taxicab Plane. International Journal of Comtemporary Mathematical Sciences 10 (2015), no. 4, 159-166 .
[10] Krause, E.F., Taxicab Geometry, Addison - Wesley Publishing Company, Menlo Park, CA (1975).

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

S. Ekmekçi

Z. Akça This is me

K. Altıntaş This is me

Publication Date

October 30, 2015

Submission Date

March 12, 2015

Acceptance Date

-

Published in Issue

Year 2015 Volume: 3 Number: 2

DOI

https://doi.org/10.36753/mathenot.421326

IZ

https://izlik.org/JA39EM46AJ

APA

Ekmekçi, S., Akça, Z., & Altıntaş, K. (2015). ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC. Mathematical Sciences and Applications E-Notes, 3(2), 27-33. https://doi.org/10.36753/mathenot.421326

AMA

1.Ekmekçi S, Akça Z, Altıntaş K. ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC. Math. Sci. Appl. E-Notes. 2015;3(2):27-33. doi:10.36753/mathenot.421326

Chicago

Ekmekçi, S., Z. Akça, and K. Altıntaş. 2015. “ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC”. Mathematical Sciences and Applications E-Notes 3 (2): 27-33. https://doi.org/10.36753/mathenot.421326.

EndNote

Ekmekçi S, Akça Z, Altıntaş K (October 1, 2015) ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC. Mathematical Sciences and Applications E-Notes 3 2 27–33.

IEEE

[1]S. Ekmekçi, Z. Akça, and K. Altıntaş, “ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC”, Math. Sci. Appl. E-Notes, vol. 3, no. 2, pp. 27–33, Oct. 2015, doi: 10.36753/mathenot.421326.

ISNAD

Ekmekçi, S. - Akça, Z. - Altıntaş, K. “ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC”. Mathematical Sciences and Applications E-Notes 3/2 (October 1, 2015): 27-33. https://doi.org/10.36753/mathenot.421326.

JAMA

1.Ekmekçi S, Akça Z, Altıntaş K. ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC. Math. Sci. Appl. E-Notes. 2015;3:27–33.

MLA

Ekmekçi, S., et al. “ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 2, Oct. 2015, pp. 27-33, doi:10.36753/mathenot.421326.

Vancouver

1.S. Ekmekçi, Z. Akça, K. Altıntaş. ON TRIGONOMETRIC FUNCTIONS AND NORM IN THE GENERALIZED TAXICAB METRIC. Math. Sci. Appl. E-Notes. 2015 Oct. 1;3(2):27-33. doi:10.36753/mathenot.421326

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