[color=#999999]This activity belongs to the [i]GeoGebra book[/i] [url=https://www.geogebra.org/m/sw2cat9w]GeoGebra Principia[/url].[/color][br][br][br]In the unit T-circle, we can define the T-radian exactly the same way we define an E-radian in the unit E-circle. To T-measure an angle, it's sufficient to measure the T-length of the corresponding (straight) arc on the unit T-circle. A T-circle has 8 T-radians.[br][br]Perpendicularity and parallelism are preserved under rotations, but, in general, T-distances are not invariant with respect to E-rotations... nor with respect to T-rotations! In fact, one of the peculiarities of T-distance is that it is sensitive to the orientation of lines: a segment, when T-rotated, no longer measures the same. The same happens with angles.

The sum of the angles in any T-triangle is 4 T-radians. A T-triangle can be equilateral or equiangular, but it can never be regular.[br][br]Any E-square is also a T-square. But because the taxicab distance is not uniform in every direction, these two T-squares have the same perimeter (though not the same area):

Trigonometric T-functions are much simpler than their Euclidean counterparts. For example, the T-sine function is not only non-transcendent but also piecewise linear. The T-tangent function is composed by piecewise E-hyperbolas.[br][list][*][color=#808080]Note: One possible expression for the T-sine function is: tsin(x) = 1 – 2 |1/2 - x/4 + 2 floor(1/4 + x/8)|. Thus, the T-cosine function can be defined as tcos(x) = tsin(x+2). The T-tangent function is a piecewise homographic function [/color][url=https://www.wikidata.org/wiki/Q60963385][img]https://www.geogebra.org/resource/scjbyz2p/0tuzuVw455vxurEw/material-scjbyz2p.png[/img][/url][color=#808080].[/color][/*][/list]

[color=#999999]Author of the construction of GeoGebra: [url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color]