### Introduction

Waves and vibrations occur in many contexts. The water waves on the sea and the vibrations of a stringed musical instrument are just two everyday examples. If the vibrations are simple ‘to and fro’ oscillations they are referred to as ‘sinusoidal’ which implies that a knowledge of trigonometry, particularly of the sine and cosine functions, is a necessary pre-requisite for dealing with their analysis. In this Section we give a brief introduction to this topic.

#### Prerequisites

- have a knowledge of the basics of trigonometry
- be aware of the standard trigonometric identities

#### Learning Outcomes

- use simple trigonometric functions to describe waves
- combine two waves of the same frequency as a single wave in amplitude-phase form

#### Contents

1 Applications of trigonometry to waves1.1 Two-dimensional motion

1.2 One-dimensional motion

1.3 Phase of a wave

1.4 Combining two wave equations