### Introduction

Our discussion so far has been limited to right-angled triangles where, apart from the right-angle itself, all angles are necessarily less than $9{0}^{∘}$ . We now extend the definitions of the trigonometric functions to any size of angle, which greatly broadens the range of applications of trigonometry.

#### Prerequisites

• have a basic knowledge of the geometry of triangles

#### Learning Outcomes

• define trigonometric functions generally
• sketch the graphs of the three main trigonometric functions: $sin,\phantom{\rule{1em}{0ex}}cos,\phantom{\rule{1em}{0ex}}tan$