5.6.1 Introduction

On mountain roads, warning signs are put up if the road goes steeply downhill. The percentage describes how steep the terrain slopes compared to a horizontal movement. Questions for the conditions of movements on an inclined plane in physics have been investigated by Galileo Galilei. The results are also relevant for technical constructions.
Trigonometric functions serve as a mathematical tool: they describe a geometric situation by means of a mathematical expression. This section describes how the relation between the percentage of the slope and the corresponding angle can be expressed. A first investigation of the properties of the trigonometric functions gives an idea of the various possible applications far beyond geometry, which will be revisited repeatedly in the later sections.