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Problem 53
Graph each function over a two-period interval. See Example 4.
y = -1 - 2 cos 5x
Problem 55
Graph each function over a two-period interval.
y = 1 - 2 cos ((1/2)x)
Problem 57
Graph each function over a two-period interval.
y = -2 + (1/2) sin 3x
Problem 61
Graph each function over a two-period interval.
y = sin [2(x + π/4) ] + 1/2
Problem 13
Graph each function over a one-period interval. See Examples 1–3.
y = tan 4x
Problem 15
Graph each function over a one-period interval. See Examples 1–3.
y = 2 tan x
Problem 17
Graph each function over a one-period interval.
y = 2 tan (¼ x)
Problem 19
Graph each function over a one-period interval.
y = cot (3x)
Problem 21
Graph each function over a one-period interval.
y = -2 tan (¼ x)
Problem 23
Graph each function over a one-period interval.
y = ½ cot (4x)
Problem 25
Graph each function over a two-period interval.
y = tan(2x - π)
Problem 27
Graph each function over a two-period interval.
y = cot (3x + π/4)
Problem 29
Graph each function over a two-period interval.
y = 1 + tan x
Problem 31
Graph each function over a two-period interval.
y = 1 - cot x
Problem 33
Graph each function over a two-period interval.
y = -1 + 2 tan x
Problem 35
Graph each function over a two-period interval.
y= -1 + (1/2) cot (2x - 3π)
Problem 37
Graph each function over a two-period interval.
y = 1 - 2 cot [2(x + π/2)]
Problem 39
Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)
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Problem 41
Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)
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Problem 43
Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)
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Problem 59
Consider the following function from Example 5. Work these exercises in order.
y = -2 - cot (x - π/4)
Based on the answer in Exercise 58 and the fact that the cotangent function has period π, give the general form of the equations of the asymptotes of the graph of y = -2 - cot (x - π/4).
Let n represent any integer.
Problem 61
Consider the following function from Example 5. Work these exercises in order.
y = -2 - cot (x - π/4)
Use the fact that the period of this function is π to find the next positive x-intercept. Round to the nearest hundredth.
Problem 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 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 3
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 frequency?
Problem 5
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin 2x
Problem 6
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = tan 3x
Problem 7
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = -½ cos 3x
Problem 8
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin 5x
Problem 9
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 1 + 2 sin ¼ x