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7.02 Graphs of trigonometric functions

Worksheet
Graphs of trigonometric functions
1

The value of \sin \theta can be represented on the given xy-plane.

a

Consider the curve y = \sin \theta:

Complete the following:

i

A rotation of 380 \degree has the same rotation as the acute angle with measure . So \sin 380 \degree = \sin ⬚.

ii

A rotation of 480 \degree has the same rotation as the obtuse angle with measure . So \sin 480 \degree = \sin ⬚.

iii

A rotation of 580 \degree has the same rotation as the reflex angle with measure . So \sin 580 \degree = \sin ⬚ \degree.

-1
1
x
-1
1
y
b

Consider the graph of y = \sin \theta for \\ 0 \leq \theta \leq 720 \degree:

Describe the nature of y = \sin \theta.

c

The number of degrees it takes for the curve to complete a full cycle is called the period of the function.

Determine the period of y = \sin \theta.

90
180
270
360
450
540
630
720
\theta
-2
-1
1
2
y
2

Consider the curve y = \sin x and state whether the following statements are true or false:

a

The graph of y = \sin x is periodic.

b

As x approaches infinity, the height of the graph approaches infinity.

c

The graph of y = \sin x is increasing between x = \left( - 90 \right) \degree and x = 0 \degree.

d

The graph of y = \sin x is symmetric about the line x = 0.

e

The graph of y = \sin x is symmetric with respect to the origin.

f

The y-values of the graph repeat after a period of 360 \degree.

-360
-180
180
360
x
-2
-1
1
2
y
3

Consider the curve y = \cos x and state whether the following statements are true or false:

a

The graph of y = \cos x is cyclic.

b

As x approaches infinity, the height of the graph approaches infinity.

c

The graph of y = \cos x is increasing between x = \left( - 180 \right) \degree and x = \left( - 90 \right) \degree.

d

The graph of y = \cos x has reflective symmetry across the line x = 0.

e

The graph of y = \cos xhas rotational symmetric with respect to the origin.

f

The y-values of the graph repeat after a period of 180 \degree.

-360
-180
180
360
x
-2
-1
1
2
y
4

Consider the curve y = \sin x:

a

State the coordinates of the y-intercept.

b

Find the maximum y-value.

c

Find the minimum y-value.

-360
-180
180
360
x
-2
-1
1
2
y
5

Consider the curve y = \cos x:

a

State the coordinates of the y-intercept.

b

Find the maximum y-value.

c

Find the minimum y-value.

-360
-180
180
360
x
-2
-1
1
2
y
6

Consider the equation y = \cos x.

a

Complete the table of values:

x0 \degree90 \degree180 \degree270 \degree360 \degree
\cos x
b

Sketch the graph of y = \cos x.

7

Consider the equation y = \sin x.

a

Complete the table of values:

x0 \degree90 \degree180 \degree270 \degree360 \degree
\sin x
b

Sketch the graph of y = \sin x.

8

Consider the equation y = \tan x.

a

State whether \tan x will be undefined in the following x-values:

i

-90\degree

ii

0 \degree

iii

90 \degree

iv

180 \degree

b

Complete the table of values:

x0 \degree45 \degree60 \degree90 \degree120 \degree135 \degree180 \degree
\tan x
c

Sketch the graph of y = \tan x.

9

Consider the graph of y = \cos x:

a

Is \cos 162 \degree positive or negative?

b

In which quadrant does an angle with measure 162 \degree lie in?

-360
-180
180
360
x
-2
-1
1
2
y
10

Consider the graph of y = \sin x:

a

Is \sin 200 \degree positive or negative?

b

In which quadrant does an angle with measure 200 \degree lie in?

-360
-180
180
360
x
-2
-1
1
2
y
11

Consider the graph of y = \tan x:

a

Is \tan 340 \degree positive or negative?

b

In which quadrant does an angle with measure 340 \degree lie in?

-360
-270
-180
-90
90
180
270
360
x
-2
-1
1
2
y
12

Consider the curve y = \sin x:

a

If one cycle of the graph of y = \sin x starts at x = 0 \degree, when does the next cycle start?

b

Find the x-value of the x-intercept in the following regions:

i

0 \degree < x < 360 \degree

ii

\left( - 360 \right) \degree < x < 0 \degree

c

True or false: As x approaches infinity, the graph of y = \sin x stays between y = - 1 and y = 1.

d

State whether the graph of y = \sin x increases or decreases in the following regions:

i

90 \degree < x < 270 \degree

ii

\left( - 270 \right) \degree < x < \left( - 90 \right) \degree

iii

\left( - 450 \right) \degree < x < \left( - 270 \right) \degree

iv

\left( - 90 \right) \degree < x < 90 \degree

v

270 \degree < x < 450 \degree

-360
-180
180
360
x
-2
-1
1
2
y
13

Consider the curve y = \cos x:

a

If one cycle of the graph of y = \cos x starts at x = \left( - 90 \right) \degree, when does the next cycle start?

b

Find the x-values of the x-intercepts in the following regions:

i

0 \degree < x < 360 \degree

ii

\left( - 360 \right) \degree < x < 0 \degree

c

True or false: As x approaches infinity, the graph of y = \cos x stays between y = - 1 and y = 1.

d

State whether the graph of y = \cos x increases or decreases in the following regions:

i

0 \degree < x < 180 \degree

ii

\left( - 180 \right) \degree < x < 0 \degree

iii

180 \degree < x < 360 \degree

iv

\left( - 360 \right) \degree < x < \left( - 180 \right) \degree

-540
-360
-180
180
360
540
x
-2
-1
1
2
y
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Outcomes

VCMMG368 (10a)

Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies.

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