MCR 3U1 – MS. CONRAD
Unit 6 - Sinusoidal Functions
NAME: ______________________
KN: /15
DATE: ______________________
AP: /20
CM: /10
KNOWLEDGE Part A – Multiple Choice (10 Marks)
Record your answers for questions 1-10 on the Scantron sheet provided.
1. A self-replicating graph results from a
a. quadratic relation
c. non-linear relation
b. linear relation
d. periodic relation
2. In the general equation y  a cos k ( x  d )  c the value of a determines the
a. phase shift (horizontal translation)
b. vertical translation
c. amplitude
d. period
3. The period of the function y  sin 4 x in degrees is
a. 360°
b. 180°
c. 90°
d. 1440°
4. The phase shift of the function y  3 sin 5( x  45) is
a. 3o to the left
b. 4o to the right
c. 45o to the right
d. 45o to the left
5. The graph of y  cos x has a maximum at
a. The origin
c. (0,1)
b. (1,0)
d. (1, 1)
6. The amplitude of the function y  4 cos 2( x  90) is
a. 2
b. 90
c. 4
d. -4
7. The range for the function y  3 sin 2( x  45)  1 is
a.  3  y  3
b.  2  y  2
c.  2  y  4
d. 4  y  5
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MCR 3U1 – MS. CONRAD
Unit 6 - Sinusoidal Functions
8. The vertical shift of the function y  25 cos(3t  4)  10 is
a. 10 down
b. 10 up
c. 25 up
d. 4 down
9. Which statement best describes the transformations that the graph of y  sin x has undergone to
become y  5 sin( 0.5 x  45)  5
a. A vertical expansion of 5, a horizontal compression by 0.5, phase shift left 45o and upwards 5
units.
b. A vertical expansion of 5, a horizontal expansion by 2, phase shift the right 45o and upwards 5
units.
c. A vertical compression by 0.5, a horizontal expansion by 2, phase shift right 45o and upwards 5
units.
d. A vertical expansion of 5, a horizontal expansion by 0.5, phase shift right 45o and upwards 5
units.
10. The graph of y  sin x passes through
a. The origin
c. (0,1)
b. (1,0)
d. (1, 1)
KNOWLEDGE PART B – Short Answer
11. For each situation given, indicate YES(Y) for those that would produce a periodic graph and
NO(N) for those that would not. (5 Marks)
a) One of Santa’s elves is monitoring the height of one of the cutting teeth on a chainsaw. The
saw is on the ground, and the chain is spinning. ______
b) The cost of riding a reindeer in the North Pole varies depending on how far you travel.
______
c) Santa is doing jumping jacks and you want to measure his height above the ground as a
function of time. ________
d) The sunset times for the North Pole for a period of 3 years. ______
e) The average monthly temperature for the North Pole over the period of a year. ______
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MCR 3U1 – MS. CONRAD
Unit 6 - Sinusoidal Functions
APPLICATION (20 Marks)
12. Answer the following questions given the cosine graph below. (7 Marks)
a) What is the max? _________ and min _________ of the function?
b) What is the amplitude of the function? ____________
c) What is the period of the function?
____________
d) What is the range of the function?
____________
e) What is the equation of the axis?
____________
f) What is the phase shift of the function? ____________
g) What is the equation for the function?
____________
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MCR 3U1 – MS. CONRAD
Unit 6 - Sinusoidal Functions
13. Graph two complete cycles of the function y  4 cos2x  90  1
(7 Marks)
14. For a person at rest, the function P(t )  20 cos 300t  100 models the blood pressure, P (t ) , in
millimeters of mercury at time t seconds.
a) What is the period of the function? What does the period represent for an individual?
(2 Marks)
b) What is the range of the function? Explain the meaning of the range in terms of a person’s
blood pressure. (2 Marks)
c) What is the blood pressure at t = 4 s. (2 Marks)
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MCR 3U1 – MS. CONRAD
Unit 6 - Sinusoidal Functions
COMMUNICATION (10 Marks)
15. Write the equation for each cosine function as described below. (4 Marks)
a) amplitude 4, period 180o, phase shift 45o to the left, vertical translation up 1
b) amplitude 3, period 720o, reflected in the x-axis, phase shift 180o to the right
16. For each of the following, state the amplitude, period, phase shift and equation of the axis.
(6 Marks)
a) y  2 sin 3( x  56)  2
b) y  3 cos 4( x  72)  3
BONUS QUESTION
Complete the lyrics to the popular Christmas song below. (2 Marks)
“Ohhhhh … You better watch out. You better not cry. You better not ______________
_________________________. Santa Clause is coming to town!”
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