### Introduction

HELM booklet 2.8. They were also used in the discussion on complex numbers in HELM booklet 10.2. We shall examine the application of polars to the description of curves, particularly conics. Some curves, spirals for example, which are very difficult to describe in terms of Cartesian coordinates $\left(x,y\right)$ are relatively easily defined in polars $\left[r,\theta \right]$ .

#### Prerequisites

• be familiar with Cartesian coordinates
• be familiar with trigonometric functions and how to manipulate then
• be able to simplify algebraic expressions and manipulate algebraic fractions

#### Learning Outcomes

• understand how Cartesian coordinates and polar coordinates are related
• find the polar form of a curve given in Cartesian form
• recognise some conics given in polar form