Trigonometry

17

17.1 Introduction EMBCR

Building on Grade 10 Trigonometry, we will look at more general formsof the the basic trigonometric

functions next. We willuse graphs and algebrato analyse the properties of these functions. Wewill

also see that different trigonometric functions are closely related through a number of mathematical

identities.

See introductory video:VMfva at http://www.everythingmaths.co.za

17.2 Graphs of Trigonometric Functions

EMBCS

Functions of the Formy=sin(kθ) EMBCT

In the equation, y = sin(kθ), k is a constant and has different effects on the graph of the function.

The general shape of the graph of functions ofthis form is shown in Figure 17.1 for the function

f(θ) = sin(2θ).

1

− 1

270 180 − − 90 − 90 180 270

Figure 17.1: Graph of f(θ) = sin(2θ) (solid line) and the graph of g(θ) = sin(θ) (dotted line).

Exercise 17 - 1

On the same set of axes, plot the following graphs:

1. a(θ) = sin0, 5 θ


2. b(θ) = sin1θ


3. c(θ) = sin1, 5 θ