Everything Maths Grade 11

17.2 CHAPTER 17. TRIGONOMETRY

Table 17.4: Table summarising general shapes and positions of graphs of functions of theform
y = sin(θ + p). The curve y = sin(θ) is plotted with a dottedline.

p > 0 p < 0

Intercepts

For functions of the form, y = sin(θ + p), the details of calculating the intercept with the y axis are
given.

The y-intercept is calculated as follows: set θ = 0◦

y = sin(θ + p)

yint = sin(0 + p)

= sin(p)

Functions of the Formy=cos(θ+p) EMBCX

In the equation, y = cos(θ + p), p 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 17.5 for the function
f(θ) = cos(θ + 30◦).

1

-1

-210-240-270-300-330 -30-60-90-120-150-180 30 60 90 120 150 180 210 240 270 300 330

Figure 17.5: Graph of f(θ) = cos(θ + 30◦) (solid line) and the graph of g(θ) = cos(θ) (dotted line).

Exercise 17 - 5

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

1. a(θ) = cos(θ− 90 ◦)


2. b(θ) = cos(θ− 60 ◦)


3. c(θ) = cos θ


4. d(θ) = cos(θ + 90◦)