Mathematics for Electrical Engineering and Computing

5

Trigonometric functions and waves

5.1 Introduction

Waves occur naturally in a number of situations: the movement of disturbed water, the passage of sound through the air, vibrations of a plucked string. If the movement of a particular particle is plotted against time, then we get the distinctive wave shape, called a sinusoid. The mathematical expression of a wave is found by using the trigonometric functions, sine and cosine. In Chapter 6 of the Background Mathematics Notes on the companion website for this book we looked at right angled triangles and defined the trigonometric ratios. The maximum angle in a right angled triangle is 90° so to find the trigonometric functions, sin(t), cos(t), and tan(t) where t can be extended over the real numbers, ...