On The Trigonometric Functions in $\mathbb{R}_{\pi 3}^{2}$

Year 2020, Volume: 8 Issue: 2, 429 - 437, 27.10.2020

Selahattin Nazlı , Ziya Akça

Abstract

In this paper, we give trigonometric functions by using reference angle in the plane $ \mathbb{R}_{\pi 3}^{2}$ associated with the induced metric $d_{\pi 3}$ that\ is a member of the family of $d_{\pi n}-$distances. Also we investigate the change of the length a line segment under the rotations in the plane $\mathbb{R} _{\pi 3}^{2}$.                                                                                                                                                                                                                                                                                                                                                 

Keywords

non-Euclidean geometry, \textbf{\ }$d_{\pi 3}-$distances, trigonometric functions in the plane $\mathbb{R} _{\pi 3}^{2}$

References

• [1] A. Bayar, R. Kaya, On Isometries of R2 pn, Hacettepe Journal of Mathematics and Statistics, Vol. 40 (5) (2011), 673-679.
• [2] A. Bayar, S. Ekmekci, M. Ozcan, On Trigonometric Functions and Cosine and Sine Rules in Taxicab Plane, International Electronic Journal of Geometry, Vol. 2 , No. 1 (2009),17–24.
• [3] A. Bayar, S. Ekmekci, On The Chinese Checker Sine and Cosine Functions, International Journal of Mathematics and Analysis, Vol. 1, No. 3 (2006), 249–259.
• [4] M. Ozcan, S. Ekmekci, A. Bayar, A Note on The Variation of The Taxicab Lengths Under Rotations, Pi Mu Epsilon Journal, Vol. 11, No, 7 (2002), 381-384.
• [5] I. Kocayusufoglu, Trigonometry on Iso-taxicab Geometry, Mathematical and Computational Applications, Vol. 5, No. 3 (2002),.201-212.
• [6] I. Kocayusufoglu, T. Ada, On The Iso-taxicab Trigonometry, Applied Sciences, Vol. 8 (2006), 101-111.
• [7] K. O. Sowell, Taxicab Geometry-a New Slant, Mathematics Magazine, 62, (1989), 238-248.
• [8] K. Thompson, T. Dray, Taxicab Angles and Trigonometry, Pi Mu Epsilon J., Vol. 11(2000), 87-97.
• [9] S. Ekmekci, Z. Akca, A. Altintas, On Trigonometric Functions and Norm in The Generalized Taxicab Metric, Math. Sciences and Applications E-Notes, Vol. 3, No. 2 (2015), 27–33.
• [10] S. Ekmekci, A. Bayar, Z. Akca, On The Plane Geometry with Generalized Absolute Value Metric, Math. Probl. Eng., Vol. 1, No. 0 (2008), 1–8.
• [11] W. E. Story, On The Non-Euclidean Trigonometry, American Journal of Mathematics, Vol. 4, No. 1 (1881), 332-335.
• [12] Z. Akca, R. Kaya, On The Taxicab Trigonometry, J. of Inst. Math. Comput. Sci. Math. Ser., Vol. 10, No. 3 (1997), 151–159.