Name: ________________________ Class: ___________________ Date: __________ ID: A
Trig Functions Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Determine the midline of the following graph.
A. y=2
B. y=3
C. y=4
D. y=5
____ 2. Determine the range of the following graph.
A. {y | 1 y 5, y R}
B. {y | –2 y 2, y R}
C. {y | 0 y 4, y R}
D. {y | y R}
____ 3. Select the function with the greatest amplitude.
A. y = 2 sin 3(x + 90°) + 5
B. y = 3 sin 2(x – 90°) – 3
1
C. y = sin (x + 90°) – 1
3
D. y = sin 0.5(x – 90°)
1
Name: ________________________ ID: A
____ 4. Select the function with the greatest period.
A. y = 2 sin 3(x + 90°) + 5
B. y = 3 sin 2(x – 90°) – 3
1
C. y = sin (x + 90°) – 1
3
D. y = sin 0.5(x – 90°)
____ 5. Select the function with the greatest maximum value.
A. y = 2 sin 3(x + 90°) + 5
B. y = 3 sin 2(x – 90°) – 3
1
C. y = sin (x + 90°) – 1
3
D. y = sin 0.5(x – 90°)
____ 6. Determine the amplitude of the following function.
y = 3 sin 2(x + 90°) – 1
A. 2
B. 3
C. 4
D. 5
____ 7. Determine the amplitude of the following function.
1
y = cos x + 12
3
1
A.
3
B. 1
C. 2
D. 12
2
Name: ________________________ ID: A
____ 8. Determine the period of the following graph.
A. 5
B. 6
C. 7
D. 8
____ 9. A sinusoidal graph has an amplitude of 10 and a maximum at the point (18, 5). Determine the
midline of the graph.
A. y=0
B. y = –5
C. y = 13
D. y=8
____ 10. Determine the period of the following function.
y = 3 sin 2(x + 90°) – 1
A. 180°
B. 360°
C. 720°
D. 1080°
____ 11. Determine the midline of the following function.
y = 3 sin 2(x + 90°) – 1
A. y=2
B. y=3
C. y=0
D. y = –1
3
Name: ________________________ ID: A
____ 12. The following data set is sinusoidal. Determine the missing value from the table.
x 1 2 3 4 5 6 7
y –5 –8 –5 –2 –5 –8
A. –2
B. –5
C. –8
D. –11
____ 13. The following data set is sinusoidal. Determine the missing value from the table.
x –3 –2 –1 0 1 2 3 6
y 1.0 1.7 2.0 1.7 1.0 0.3 0.0
A. 0.0
B. 0.3
C. 1.7
D. 2.0
____ 14. The amount of daylight in a town can be modelled by the sinusoidal function
d(t) = 4.37 cos 0.017t + 12.52
where d(t) represents the hours of daylight and t represents the number of days since June 20, 2012.
How many hours of daylight should be expected on June 20, 2013?
A. 16.80 h
B. 16.84 h
C. 16.88 h
D. 16.92 h
____ 15. The height of a mass attached to a spring can be modelled by the sinusoidal function
h(t) = 84 – 6.7 cos 24.8t
where h(t) represents the height in centimetres and t represents the time in seconds.
What is the height of the mass after 10 s?
A. 77.4 cm
B. 84.0 cm
C. 86.9 cm
D. 90.6 cm
4
Name: ________________________ ID: A
Short Answer
1. a) Determine the period of the following graph.
b) Would the graph be most simply represented by a sine or cosinge function? Why?
2. Determine the period , horizontal shift and range of the following function.
y = 10 cos 4(x – 180°) + 2
Period: __________ Range: __________ Horizontal shift: ___________
3. A seat’s position on a Ferris wheel can be modelled by the function
y = 18 cos 160.4(x +68.75) + 21,
where y represents the height in feet and x represents the time in minutes.
_____a) Determine the diameter of the Ferris wheel.
_____b) What is the greatest height reached by the wheel?
._____b) What is the period of this function? What is its meaning in this context? (use 2 )
* sketch the graph:
5
Name: ________________________ ID: A
Problem
1. Sketch a possible graph of a sinusoidal function with the following set of characteristics. Explain
your decision.
Domain: {x | 0 x 720, x R}
Maximum value: 5
Minimum value: –5
Period: 720°
y-intercept: 0
*What is a possible equation for this function? ________________________
2. The graph of a sinusoidal function is shown.
a) Describe this graph by determining its range, period, the equation of its midline, and its
amplitude. Show your work.
6
Name: ________________________ ID: A
3. Jeremy’s gymnastics coach graphs one particular series of jumps. Describe Jeremy’s jumps using
the graph. Show your work.
4. Describe the graph of the following function by stating the amplitude, equation of its midline,
range, and period and horizontal shift (translation).
*If you wanted to write this as a sine function instead, how could you rewrite the function?
y = 6 cos 8(x – 1.4) – 4
7
ID: A
Trig Functions Review
Answer Section
MULTIPLE CHOICE
1. B
2. A
3. B
4. D
5. A
6. B
7. B
8. D
9. B
10. A
11. D
12. B
13. C
14. C
15. D
SHORT ANSWER
1. 300°
Cosine because the y-int is a max point, or is not zero.
2. Period: 90°; Range: -2</=y</=8; Horizontal Shift: Right 180
3. a) 36 m; b) 39m; c) 360/2.8 = 128.6 - The number of minutes for a complete revolution.
1
ID: A
PROBLEM
1. Answers may vary. Sample answer:
The period is two thirds the domain, so 1.5 cycles are included.
The graph has a maximum of 5 and a minimum of –5.
The graph starts at the point (0, 0):
2. Range:
Minimum value = –8
Maximum value = 4
The range of the graph is {y | –8 y 4, y R}.
Equation of the midline (halfway between the maximum and minimum values):
maximum value + minimumvalue
y=
2
4 (8)
y=
2
y = –2
Amplitude (the vertical distance between the maximum value and the midline):
Amplitude = 4 – (–2)
Amplitude = 6
2
ID: A
3. Range:
Minimum value = 1
Maximum value = 7
The range of the graph is {y | 1 y 7, y R}.
Equation of the midline (halfway between the maximum and minimum values):
maximum value + minimumvalue
y=
2
71
y=
2
y=4
Amplitude (the vertical distance between the maximum value and the midline):
Amplitude = 7 – 4
Amplitude = 3
Period:
There is a maximum value at 13 and a maximum value at 17.
Period = 17 – 13
Period = 4
4. y = a cos b(x – c) + d
y = 6 cos 8(x – 1.4) – 4
a = 6, b = 8, c = 1.4, d = –4
The amplitude of the graph is a, which is 6.
The equation of the midline is y = d, or y = –4.
Minimum value = d – a Maximum value = d + a
Minimum value = –4 – 6 Maximum value = –4 + 6
Minimum value = –10 Maximum value = 2
The range of the graph is {y | –10 y 2, y R}.
Since b = 8, the graph completes 8 cycles in 360° or 2 radians.
360
Period =
b
360
Period =
8
Period = 45°
