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Problem 4.1
Fill in the blank(s) to correctly complete each sentence.
The graph of y = sin (x + π/4) is obtained by shifting the graph of y = sin x ______ unit(s) to the ________ (right/left).
Problem 4.1
An object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.
𝒮(t) = 5 cos 2t
What is the amplitude of this motion?
Problem 4.10
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 3 - ¼ cos ⅔ x
Problem 4.11
Graph each function over a one-period interval.
y = 3 sec [(1/4)x]
Problem 4.11
Match each function with its graph in choices A–I. (One choice will not be used.)
y = cos (x - π/4)
A. <IMAGE> B. <IMAGE> C. <IMAGE>
D. <IMAGE> E. <IMAGE> F. <IMAGE>
G. <IMAGE> H. <IMAGE> I. <IMAGE>
Problem 4.11
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 3 cos (x + π/2)
Problem 4.12
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = -sin (x - 3π/4)
Problem 4.13
Graph each function over the interval [-2π, 2π]. Give the amplitude. See Example 1.
y = 2 cos x
Problem 4.13
Graph each function over a one-period interval. See Examples 1–3.
y = tan 4x
Problem 4.13
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = (1/2)csc (2x - π/4)
Problem 4.14
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sec(πx - 2π)
Problem 4.15
Graph each function over a one-period interval.
y = csc (x - π/4)
Problem 4.15
Graph each function over the interval [-2π, 2π]. Give the amplitude. See Example 1.
y = ⅔ sin x
Problem 4.15
Graph each function over a one-period interval. See Examples 1–3.
y = 2 tan x
Problem 4.15
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 1/3 tan (3x - π/3)
Problem 4.16
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = cot (x/2 + 3π/4)
Problem 4.16
Match each function with its graph in choices A–I. (One choice will not be used.)
y = -1 + cos x
A. <IMAGE> B. <IMAGE> C. <IMAGE>
D. <IMAGE> E. <IMAGE> F. <IMAGE>
G. <IMAGE> H. <IMAGE> I. <IMAGE>
Problem 4.17
Graph each function over a one-period interval.
y = sec (x + π/4)
Problem 4.17
Graph each function over a one-period interval.
y = 2 tan (¼ x)
Problem 4.19
Graph each function over the interval [-2π, 2π]. Give the amplitude. See Example 1.
y = -2 sin x
Problem 4.19
Graph each function over a one-period interval.
y = csc((1/2)x - π/4)
Problem 4.19
Graph each function over a one-period interval.
y = cot (3x)
Problem 4.19
Match each function in Column I with the appropriate description in Column II.
I
y = 3 sin(2x - 4)
II
A. amplitude = 2, period = π/2, phase shift = ¾
B. amplitude = 3, period = π, phase shift = 2
C. amplitude = 4, period = 2π/3, phase shift = ⅔
D. amplitude = 2, period = 2π/3, phase shift = 4⁄3
Problem 4.2
An object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.
𝒮(t) = 5 cos 2t
What is the period of this motion?
Problem 4.2
Fill in the blank(s) to correctly complete each sentence.
The graph of y = cos (x - π/6) is obtained by shifting the graph of y = cos x ______ unit(s) to the ________ (right/left).
Problem 4.21
Graph each function over a one-period interval.
y = (1/2) csc (2x + π/2)
Problem 4.21
Graph each function over a one-period interval.
y = -2 tan (¼ x)
Problem 4.21
Identify the circular function that satisfies each description.
period is π; function is decreasing on the interval (0, π)
Problem 4.21
Match each function in Column I with the appropriate description in Column II.
I
y = -4 sin(3x - 2)
II
A. amplitude = 2, period = π/2, phase shift = ¾
B. amplitude = 3, period = π, phase shift = 2
C. amplitude = 4, period = 2π/3, phase shift = ⅔
D. amplitude = 2, period = 2π/3, phase shift = 4⁄3
Problem 4.23
Graph each function over a one-period interval.
y = 2 + 3 sec (2x - π)
