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Deck 8: Graphs of the Trigonometric Functions
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Question
Use the Pythagorean identities to simplify the expression. 
A)
B)
C)
D) 1
E)
A)
B)
C)
D) 1
E)
Question
Refer to the graph of 
in the figure. Specify the coordinates of the point I. 
A)
B)
C)
D)
E)
in the figure. Specify the coordinates of the point I. A)
B)
C)
D)
E)
Question
Determine whether the equation for the graph has the form 
or 
( with 
) and then find the values of 
and 
. 
A)
B)
C)
D)
E)
or ( with ) and then find the values of and . A)
B)
C)
D)
E)
Question
State whether the function 
is increasing or decreasing on the interval. 
A) increasing
B) decreasing
is increasing or decreasing on the interval. A) increasing
B) decreasing
Question
State whether the function 
is increasing or decreasing on the interval. 
A) decreasing
B) increasing
is increasing or decreasing on the interval. A) decreasing
B) increasing
Question
Refer to the graph of 
in the figure. Specify the coordinates of the point I. 
A)
B)
C)
D)
E)
in the figure. Specify the coordinates of the point I. A)
B)
C)
D)
E)
Question
A mass on a smooth tabletop is attached to a spring, as shown in the figure. The coordinate system has been chosen so that the equilibrium position of the mass corresponds to 
. Assume that the simple harmonic motion is described by the equation 
, where s is in centimeters and t is in seconds. Determine which table describes the s-coordinate of the mass at each of the following times: 
0 sec, 0.5 sec, 1 sec, and 2 sec. (One of these coordinates will involve a radical sign; for this case, use a calculator and round the final answer to two decimal places.) 
A)
B)
C)
D)
E)
. Assume that the simple harmonic motion is described by the equation , where s is in centimeters and t is in seconds. Determine which table describes the s-coordinate of the mass at each of the following times: 0 sec, 0.5 sec, 1 sec, and 2 sec. (One of these coordinates will involve a radical sign; for this case, use a calculator and round the final answer to two decimal places.) A)
B)
C)
D)
E)
Question
Consider the function 
. Specify the phase shift.
A)
B)
C)
D)
E)
. Specify the phase shift.A)
B)
C)
D)
E)
Question
Consider the function 
on the interval 
. Specify the intervals in which the function is increasing.
A)
B)
C)
D)
E)
on the interval . Specify the intervals in which the function is increasing.A)
B)
C)
D)
E)
Question
Consider the function 
. Specify the period.
A)
B)
C)
D)
E)
. Specify the period.A)
B)
C)
D)
E)
Question
Consider the function 
on the interval 
. Determine the 
-intercepts by giving the 
-coordinate(s).
A)
B)
C)
D)
E) there are no
-intercepts
on the interval . Determine the -intercepts by giving the -coordinate(s).A)
B)
C)
D)
E) there are no
-intercepts Question
Given: 
. Determine the right side of the identity equation.
A)
B)
C)
D)
E)
. Determine the right side of the identity equation.A)
B)
C)
D)
E)
Question
Consider the function 
. Specify the amplitude.
A)
B)
C)
D)
E)
. Specify the amplitude.A)
B)
C)
D)
E)
Question
Consider the function 
. Specify the amplitude.
A) 1
B) 4
C) 5
D) 8
E) 2
. Specify the amplitude.A) 1
B) 4
C) 5
D) 8
E) 2
Question
Consider the function 
. Specify the period.
A)
B)
C)
D)
E)
. Specify the period.A)
B)
C)
D)
E)
Question
Compute 
, 
, and 
. 
and 
A)
, 
, 
B)
, 
, 
C)
, 
, 
D)
, 
, 
E)
, 
, 
, , and . and A)
, , B)
, , C)
, , D)
, , E)
, , Question
Use the Pythagorean identities to simplify the expression. 
A)
B)
C)
D)
E) 1
A)
B)
C)
D)
E) 1
Question
Consider the function 
. Specify the period.
A)
B)
C)
D)
E)
. Specify the period.A)
B)
C)
D)
E)
Question
Specify the period and amplitude for the function. 
A) period: 8; amplitude: 8
B) period: 4; amplitude: 16
C) period: 2; amplitude: 16
D) period: 4; amplitude: 8
E) period: 2; amplitude: 8
A) period: 8; amplitude: 8
B) period: 4; amplitude: 16
C) period: 2; amplitude: 16
D) period: 4; amplitude: 8
E) period: 2; amplitude: 8
Question
Consider the function 
on the interval 
. Determine the 
-intercepts by giving the 
-coordinate(s).
A)
B)
C)
D)
E)
on the interval . Determine the -intercepts by giving the -coordinate(s).A)
B)
C)
D)
E)
Question
Graph the function for one period, and show (or specify) intercepts and asymptotes. 
A)x-intercept: none; y-intercept:
; asymptotes: 
and 
B) x-intercept: none; y-intercept:
; asymptotes: 
and 
C) x-intercept:
; y-intercept: 
; asymptotes: 
and 
D) x-intercept:
; y-intercept: 
; asymptotes: 
and 
E) x-intercept:
; y-intercept: 
; asymptotes: 
and 
A)x-intercept: none; y-intercept:
; asymptotes: and B) x-intercept: none; y-intercept:
; asymptotes: and C) x-intercept:
; y-intercept: ; asymptotes: and D) x-intercept:
; y-intercept: ; asymptotes: and E) x-intercept:
; y-intercept: ; asymptotes: and Question
Graph the function for one period, and show (or specify) intercepts and asymptotes. 
A) x-intercept: none; y-intercept: none; asymptotes:
, 
and 
B) x-intercept: none; y-intercept: none; asymptotes:
, 
and 
C) x-intercept: none; y-intercept: none; asymptotes:
and 
Chapter 8
Answer Section
MULTIPLE CHOICE
D) x-intercept: none; y-intercept: none; asymptotes:
, 
and 
E) x-intercept: none; y-intercept: none; asymptotes:
, 
and 
A) x-intercept: none; y-intercept: none; asymptotes:
, and B) x-intercept: none; y-intercept: none; asymptotes:
, and C) x-intercept: none; y-intercept: none; asymptotes:
and Chapter 8
Answer Section
MULTIPLE CHOICE
D) x-intercept: none; y-intercept: none; asymptotes:
, and E) x-intercept: none; y-intercept: none; asymptotes:
, and Question
Graph the function for one period, and show (or specify) intercepts and asymptotes. 
A) x-intercept: none; y-intercept: none; asymptotes:
, 
and 
B) x-intercept: none; y-intercept: none; asymptotes:
and 
C) x-intercept: none; y-intercept: none; asymptotes:
, 
and 
D) x-intercept: none; y-intercept: none; asymptotes:
, 
and 
E) x-intercept: none; y-intercept: none; asymptotes:
, 
and 
A) x-intercept: none; y-intercept: none; asymptotes:
, and B) x-intercept: none; y-intercept: none; asymptotes:
and C) x-intercept: none; y-intercept: none; asymptotes:
, and D) x-intercept: none; y-intercept: none; asymptotes:
, and E) x-intercept: none; y-intercept: none; asymptotes:
, and Question
Graph the function for one period, and show (or specify) the intercepts and the asymptotes. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Graph the function for one period, and show (or specify) the intercepts and the asymptotes. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Deck 8: Graphs of the Trigonometric Functions
1
Use the Pythagorean identities to simplify the expression.
A)
B)
C)
D) 1
E)
A)
B)
C)
D) 1
E)
2
Refer to the graph of in the figure. Specify the coordinates of the point I.
A)
B)
C)
D)
E)
in the figure. Specify the coordinates of the point I. A)
B)
C)
D)
E)
3
Determine whether the equation for the graph has the form or ( with ) and then find the values of and .
A)
B)
C)
D)
E)
or ( with ) and then find the values of and . A)
B)
C)
D)
E)
4
State whether the function is increasing or decreasing on the interval.
A) increasing
B) decreasing
is increasing or decreasing on the interval. A) increasing
B) decreasing
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5
State whether the function is increasing or decreasing on the interval.
A) decreasing
B) increasing
is increasing or decreasing on the interval. A) decreasing
B) increasing
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6
Refer to the graph of in the figure. Specify the coordinates of the point I.
A)
B)
C)
D)
E)
in the figure. Specify the coordinates of the point I. A)
B)
C)
D)
E)
Unlock Deck
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7
A mass on a smooth tabletop is attached to a spring, as shown in the figure. The coordinate system has been chosen so that the equilibrium position of the mass corresponds to . Assume that the simple harmonic motion is described by the equation , where s is in centimeters and t is in seconds. Determine which table describes the s-coordinate of the mass at each of the following times: 0 sec, 0.5 sec, 1 sec, and 2 sec. (One of these coordinates will involve a radical sign; for this case, use a calculator and round the final answer to two decimal places.)
A)
B)
C)
D)
E)
. Assume that the simple harmonic motion is described by the equation , where s is in centimeters and t is in seconds. Determine which table describes the s-coordinate of the mass at each of the following times: 0 sec, 0.5 sec, 1 sec, and 2 sec. (One of these coordinates will involve a radical sign; for this case, use a calculator and round the final answer to two decimal places.) A)
B)
C)
D)
E)
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8
Consider the function . Specify the phase shift.
A)
B)
C)
D)
E)
. Specify the phase shift.A)
B)
C)
D)
E)
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9
Consider the function on the interval . Specify the intervals in which the function is increasing.
A)
B)
C)
D)
E)
on the interval . Specify the intervals in which the function is increasing.A)
B)
C)
D)
E)
Unlock Deck
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10
Consider the function . Specify the period.
A)
B)
C)
D)
E)
. Specify the period.A)
B)
C)
D)
E)
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11
Consider the function on the interval . Determine the -intercepts by giving the -coordinate(s).
A)
B)
C)
D)
E) there are no -intercepts
on the interval . Determine the -intercepts by giving the -coordinate(s).A)
B)
C)
D)
E) there are no
-intercepts Unlock Deck
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12
Given: . Determine the right side of the identity equation.
A)
B)
C)
D)
E)
. Determine the right side of the identity equation.A)
B)
C)
D)
E)
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13
Consider the function . Specify the amplitude.
A)
B)
C)
D)
E)
. Specify the amplitude.A)
B)
C)
D)
E)
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14
Consider the function . Specify the amplitude.
A) 1
B) 4
C) 5
D) 8
E) 2
. Specify the amplitude.A) 1
B) 4
C) 5
D) 8
E) 2
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15
Consider the function . Specify the period.
A)
B)
C)
D)
E)
. Specify the period.A)
B)
C)
D)
E)
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16
Compute , , and . and
A) , ,
B) , ,
C) , ,
D) , ,
E) , ,
, , and . and A)
, , B)
, , C)
, , D)
, , E)
, , Unlock Deck
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17
Use the Pythagorean identities to simplify the expression.
A)
B)
C)
D)
E) 1
A)
B)
C)
D)
E) 1
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18
Consider the function . Specify the period.
A)
B)
C)
D)
E)
. Specify the period.A)
B)
C)
D)
E)
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19
Specify the period and amplitude for the function.
A) period: 8; amplitude: 8
B) period: 4; amplitude: 16
C) period: 2; amplitude: 16
D) period: 4; amplitude: 8
E) period: 2; amplitude: 8
A) period: 8; amplitude: 8
B) period: 4; amplitude: 16
C) period: 2; amplitude: 16
D) period: 4; amplitude: 8
E) period: 2; amplitude: 8
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20
Consider the function on the interval . Determine the -intercepts by giving the -coordinate(s).
A)
B)
C)
D)
E)
on the interval . Determine the -intercepts by giving the -coordinate(s).A)
B)
C)
D)
E)
Unlock Deck
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21
Graph the function for one period, and show (or specify) intercepts and asymptotes.
A)x-intercept: none; y-intercept:
; asymptotes: and
B) x-intercept: none; y-intercept:
; asymptotes: and
C) x-intercept: ; y-intercept: ; asymptotes: and
D) x-intercept: ; y-intercept: ; asymptotes: and
E) x-intercept: ; y-intercept: ; asymptotes: and
A)x-intercept: none; y-intercept:
; asymptotes: and B) x-intercept: none; y-intercept:
; asymptotes: and C) x-intercept:
; y-intercept: ; asymptotes: and D) x-intercept:
; y-intercept: ; asymptotes: and E) x-intercept:
; y-intercept: ; asymptotes: and Unlock Deck
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22
Graph the function for one period, and show (or specify) intercepts and asymptotes.
A) x-intercept: none; y-intercept: none; asymptotes: , and
B) x-intercept: none; y-intercept: none; asymptotes: , and
C) x-intercept: none; y-intercept: none; asymptotes: and
Chapter 8
Answer Section
MULTIPLE CHOICE
D) x-intercept: none; y-intercept: none; asymptotes: , and
E) x-intercept: none; y-intercept: none; asymptotes: , and
A) x-intercept: none; y-intercept: none; asymptotes:
, and B) x-intercept: none; y-intercept: none; asymptotes:
, and C) x-intercept: none; y-intercept: none; asymptotes:
and Chapter 8
Answer Section
MULTIPLE CHOICE
D) x-intercept: none; y-intercept: none; asymptotes:
, and E) x-intercept: none; y-intercept: none; asymptotes:
, and Unlock Deck
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23
Graph the function for one period, and show (or specify) intercepts and asymptotes.
A) x-intercept: none; y-intercept: none; asymptotes: , and
B) x-intercept: none; y-intercept: none; asymptotes: and
C) x-intercept: none; y-intercept: none; asymptotes: , and
D) x-intercept: none; y-intercept: none; asymptotes: , and
E) x-intercept: none; y-intercept: none; asymptotes: , and
A) x-intercept: none; y-intercept: none; asymptotes:
, and B) x-intercept: none; y-intercept: none; asymptotes:
and C) x-intercept: none; y-intercept: none; asymptotes:
, and D) x-intercept: none; y-intercept: none; asymptotes:
, and E) x-intercept: none; y-intercept: none; asymptotes:
, and Unlock Deck
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24
Graph the function for one period, and show (or specify) the intercepts and the asymptotes.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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25
Graph the function for one period, and show (or specify) the intercepts and the asymptotes.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
