Everything Maths Grade 11

CHAPTER 17. TRIGONOMETRY 17.2

4. d(θ) = sin2θ


5. e(θ) = sin2, 5 θ

Use your results to deduce the effect of k.

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You should have foundthat the value of k affects the period or frequency of the graph. Notice that in
the case of the sine graph, the period (length ofone wave) is given by^360

◦

k.

These different properties are summarised in Table 17.1.

Table 17.1: Table summarising general shapes and positions of graphs of functions of theform
y = sin(kx). The curve y = sin(x) is shown as a dotted line.

k > 0 k < 0

Domain and Range

For f(θ) = sin(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) = sin(kθ) is{f(θ) : f(θ)∈ [−1;1]}.

Intercepts

For functions of the form, y = sin(kθ), the details of calculating the intercepts withthe y axis are
given.

There are many x-intercepts.

The y-intercept is calculated by setting θ = 0:

y = sin(kθ)

yint = sin(0)

= 0