Download Part 1 – Selected Response 3 3 ( 3) cos ( 90 ) 2 4 y x − = − ° ?

Mathematics 2205
2005 – 2006
Work Sample #4
Page 1 of 11
Sections 3.1 & 3.2
Part 1 – Selected Response
Complete each of the following with the best fitting answer and place the
answer on the answer sheet provided.
1.
Which of the following statements described the graph below?
y
2
1
– 180
180
360
540
720
900
1080 x
– 1
A.
B.
C.
D.
2.
Which of the following statements regarding the graphs of the
sine function and the cosine function is true?
A.
B.
C.
D.
3.
sinusoidal
periodic
periodic and sinusoidal
neither periodic nor sinusoidal
the amplitude of both graphs is 360°
the period of both graphs is 180°
the sinusoidal axis is x = 0 for both curves
the cosine curve is the same as the sine curve translated 90°
left
What is the period for the equation
A.
B.
C.
D.
480°
240°
270°
540°
3
3
( y − 3) = cos ( x − 90°) ?
2
4
Mathematics 2205
2005 – 2006
4.
Work Sample #4
Page 2 of 11
Sections 3.1 & 3.2
Which statement applies to the graph below?
y
5
4
3
2
1
– 180 – 90
90
180
270
360
450
540
630
720
x
– 1
A.
B.
C.
D.
5.
the amplitude is 2, therefore the VT is 2 units up
the sinusoidal axis is y = 3, therefore the VS factor is 1/3
the period is 180°, therefore the HS factor is ½
the local minimum is 1 giving a HT 1 unit down
If the graph of the function shown below has the equation
1
a
A.
( y − d ) = sin [ b ( x − c ) ] , determine the value of
8
B.
4
C.
22.5
a.
( a > 0)
D.
45
Mathematics 2205
2005 – 2006
Work Sample #4
Page 3 of 11
Sections 3.1 & 3.2
6. What is the sinusoidal axis for the graph of the following equation?
1 y − 4 = cos ⎡ 2 ( x − 45°)⎤
⎢
⎥
)
2(
⎣⎢ 3
⎦⎥
A. y = 45°
B. y = 4
C. y = 2
D. y =
3
2
7. A red flag is attached to one of the propellers on a windmill and its
height above the ground is recorded on the graph below. What is the
speed of rotation?
A. 2.1m/s
B. 0.67m/s
C. 1.3m/s
D. 0.75m/s
8. What is the horizontal stretch factor for the equation?
2
y = −4 cos ( x − 60°) − 2
5
A.
5
2
B. 4
C. -4
D. −
1
4
Mathematics 2205
2005 – 2006
Work Sample #4
Page 4 of 11
Sections 3.1 & 3.2
9. Which of the following equations describes this graph?
y
5
4
3
2
1
– 180
180
360
540
720 x
– 1
A. y = 3cos3( x + 90°) + 3
C. y = 2cos 2( x − 90°) + 3
B. y = 2cos 2( x + 90°) + 3
D. y = 3cos 2( x − 90°) − 3
10.
What is the range of the graph with equation
y = 2sin 2( x + 90°) + 2 ?
A. { y 0 ≤ y ≤ 4, y ∈ R}
B.
{ y y ≤ 360}
C.
D.
{ y y ∈ R}
{ y 0 ≤ y ≤ 180}
Mathematics 2205
2005 – 2006
Work Sample #4
Page 5 of 11
Sections 3.1 & 3.2
Name: _________________
Page ___ of ___
Part 1 Answer Sheet
Place your answers for part in the space provided.
1. _______________
6. _______________
2. _______________
7. _______________
3. _______________
8. _______________
4. _______________
9. _______________
5. _______________
10. _______________
Mathematics 2205
2005 – 2006
Sections 3.1 & 3.2
Name: _________________
Part 2
Work Sample #4
Page 6 of 11
Page ___ of ___
Answer each of the following questions in the space
provided. Show all workings where appropriate as marks may
be given for partially correct answers (10 marks each)
1. For each of the following equations sketch the graph using the
mapping rule method and state the period, sinusoidal axis, amplitude,
and the maximum and minimum values:
A.
1
( y − 1) = sin 3( x − 90°)
2
y
5
4
3
2
1
– 90
90
180
270
– 1
Sinusoidal Axis is:
Amplitude =
Local Maximum =
Period =
Local Minimum =
360
x
Mathematics 2205
2005 – 2006
Sections 3.1 & 3.2
Name: _________________
B.
Work Sample #4
Page 7 of 11
Page ___ of ___
1
( y + 2 ) = cos3( x − 60°)
2
y
1
– 90
90
180
270
– 1
– 2
– 3
– 4
– 5
Sinusoidal Axis is:
Amplitude =
Local Maximum =
Period =
Local Minimum =
360
x
Mathematics 2205
2005 – 2006
Work Sample #4
Page 8 of 11
Sections 3.1 & 3.2
Name: _________________
Page ___ of ___
2. For each of the following graphs determine the following:
(i)
(ii)
(iii)
(iv)
The vertical and horizontal translations
The vertical and horizontal stretch factors
The equation of the graph as a sine function
The equation of the graph as a cosine function
A.
y
6
5
4
3
2
1
– 90
90
– 1
180
270
360
x
Mathematics 2205
2005 – 2006
Work Sample #4
Page 9 of 11
Sections 3.1 & 3.2
Name: _________________
Page ___ of ___
B.
y
6
5
4
3
2
1
– 90
90
– 1
– 2
180
270
360
x
Mathematics 2205
2005 – 2006
Sections 3.1 & 3.2
Name: _________________
Work Sample #4
Page 10 of 11
Page ___ of ___
3. A piston in an engine is 12cm from the crank shaft at 0s. Once the
piston is set in motion it is 36cm from the crank shaft 0.30s later.
The motion of the piston is approximated by a sinusoidal function
where d is the distance from the crank shaft and t is the elapsed
time.
A. Draw a table of values and sketch a graph for the above situation
showing at least two cycles of the graph.
y
x
Mathematics 2205
2005 – 2006
Sections 3.1 & 3.2
Name: _________________
Work Sample #4
Page 11 of 11
Page ___ of ___
B. From the graph in part A, determine equations for sinusoidal functions
that give d as a function of t in transformational forms of both the
sine function AND the cosine function.