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

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 $\mathbb{R} _{\pi 3}^{2}$.