Indietro
Problema 53
Graph each function over a two-period interval. See Example 4.
y = -1 - 2 cos 5x
Problema 55
Graph each function over a two-period interval.
y = 1 - 2 cos ((1/2)x)
Problema 57
Graph each function over a two-period interval.
y = -2 + (1/2) sin 3x
Problema 61
Graph each function over a two-period interval.
y = sin [2(x + π/4) ] + 1/2
Problema 13
Graph each function over a one-period interval. See Examples 1–3.
y = tan 4x
Problema 15
Graph each function over a one-period interval. See Examples 1–3.
y = 2 tan x
Problema 17
Graph each function over a one-period interval.
y = 2 tan (¼ x)
Problema 19
Graph each function over a one-period interval.
y = cot (3x)
Problema 21
Graph each function over a one-period interval.
y = -2 tan (¼ x)
Problema 23
Graph each function over a one-period interval.
y = ½ cot (4x)
Problema 25
Graph each function over a two-period interval.
y = tan(2x - π)
Problema 27
Graph each function over a two-period interval.
y = cot (3x + π/4)
Problema 29
Graph each function over a two-period interval.
y = 1 + tan x
Problema 31
Graph each function over a two-period interval.
y = 1 - cot x
Problema 33
Graph each function over a two-period interval.
y = -1 + 2 tan x
Problema 35
Graph each function over a two-period interval.
y= -1 + (1/2) cot (2x - 3π)
Problema 37
Graph each function over a two-period interval.
y = 1 - 2 cot [2(x + π/2)]
Problema 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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Problema 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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Problema 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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Problema 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.
Problema 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.
Problema 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?
Problema 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?
Problema 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?
Problema 5
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin 2x
Problema 6
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = tan 3x
Problema 7
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = -½ cos 3x
Problema 8
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin 5x
Problema 9
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 1 + 2 sin ¼ x