Everything Maths Grade 11

17.2 CHAPTER 17. TRIGONOMETRY

Functions of the Formy=cos(kθ) EMBCU

In the equation, y = cos(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 17.2 for the function
f(θ) = cos(2θ).

1

-1

-225-270-315 -45-90-135-180 45 90 135 180 225 270 315

Figure 17.2: Graph of f(θ) = cos(2θ) (solid line) and the graph of g(θ) = cos(θ) (dotted line).

Exercise 17 - 2

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

1. a(θ) = cos0, 5 θ


2. b(θ) = cos1θ


3. c(θ) = cos1, 5 θ


4. d(θ) = cos2θ


5. e(θ) = cos2, 5 θ

Use your results to deduce the effect of k.

More practice video solutions or help at http://www.everythingmaths.co.za

(1.) 013h

You should have foundthat the value of k affects the period or frequency of the graph. The period of
the cosine graph is givenby^360

◦

k.

These different properties are summarised in Table 17.2.

Domain and Range

For f(θ) = cos(kθ), the domain is{θ : θ∈R} because there is no value of θ∈R for which f(θ) is
undefined.

The range of f(θ) = cos(kθ) is{f(θ) : f(θ)∈ [−1;1]}.