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Problem 4.23
Graph each function over a one-period interval.
y = ½ cot (4x)
Problem 4.24
Graph each function over a one-period interval.
y = ½ sec x
Problem 4.24
Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.
y = sin ⅔ x
Problem 4.25
Graph each function over a one-period interval.
y = 1 - (1/2) csc (x - 3π/4)
Problem 4.25
Graph each function over a two-period interval.
y = tan(2x - π)
Problem 4.26
Graph each function over a one-period interval.
y = -2 cos x
Problem 4.27
Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.
y = sin 3x
Problem 4.27
Determine an equation for each graph.
Problem 4.27
Graph each function over a two-period interval.
y = cot (3x + π/4)
Problem 4.27
Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.
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Problem 4.27
Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.
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Problem 4.28
Graph each function over a one-period interval.
y = -1 + csc x
Problem 4.29
Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.
y = 2 sin ¼ x
Problem 4.29
Determine an equation for each graph.
Problem 4.29
Graph each function over a two-period interval.
y = 1 + tan x
Problem 4.29
Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.
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Problem 4.3
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 4.3
Fill in the blank(s) to correctly complete each sentence.
The graph of y = 4 sin x is obtained by stretching the graph of y = sin x vertically by a factor of ________.
Problem 4.31
Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.
y = -2 cos 3x
Problem 4.31
Determine an equation for each graph.
Problem 4.31
Graph each function over a two-period interval.
y = 1 - cot x
Problem 4.31
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin (x + π)
Problem 4.33
Graph each function over a two-period interval.
y = -1 + 2 tan x
Problem 4.33
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = -¼ cos (½ x + π/2)
Problem 4.35
Decide whether each statement is true or false. If false, explain why.
The graph of y = sec x in Figure 37 suggests that sec(-x) = sec x for all x in the domain of sec x.
Problem 4.35
Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.
y = -2 sin 2 πx
Problem 4.35
Graph each function over a two-period interval.
y= -1 + (1/2) cot (2x - 3π)
Problem 4.35
For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 3 cos [π/2 (x - ½)]
Problem 4.37
Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.
y = ½ cos π x
2
Problem 4.37
Graph each function over a two-period interval.
y = 1 - 2 cot [2(x + π/2)]