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Blitzer 3rd EditionCh. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric FunctionsProblem 1
Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 4 sin x
Problem 3
Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 1/3 sin x
Problem 5
Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = -3 sin x
Problem 9
Determine the amplitude and period of each function. Then graph one period of the function. y = 3 sin (1/2) x
Problem 13
Determine the amplitude and period of each function. Then graph one period of the function. y = -3 sin 2πx
Problem 15
In Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function. y = -sin 2/3 x
Problem 17
In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = sin(x − π)
Problem 18
Determine the amplitude, period, and phase shift of each function. Then graph one period of the function.
y = sin (x − π/2)
Problem 21
In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 3 sin(2x − π)
Problem 23
In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 1/2 sin(x + π/2)
Problem 24
Determine the amplitude, period, and phase shift of each function. Then graph one period of the function.
y = 1/2 sin(x + π)
Problem 25
In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −2 sin(2x + π/2)
Problem 27
Determine the amplitude, period, and phase shift of each function. Then graph one period of the function.
y = 3 sin(πx + 2)
Problem 29
In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −2 sin(2πx + 4π)
Problem 31
In Exercises 31–34, determine the amplitude of each function. Then graph the function and y = cos x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 2 cos x
Problem 35
In Exercises 35–42, determine the amplitude and period of each function. Then graph one period of the function. y = cos 2x
Problem 37
In Exercises 35–42, determine the amplitude and period of each function. Then graph one period of the function. y = 4 cos 2πx
Problem 39
In Exercises 35–42, determine the amplitude and period of each function. Then graph one period of the function. y = -4 cos 1/2 x
Problem 43
In Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = cos(x − π/2)
Problem 44
Determine the amplitude, period, and phase shift of each function. Then graph one period of the function.
y = cos(x + π/2)
Problem 45
In Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 3 cos(2x − π)
Problem 46
Determine the amplitude, period, and phase shift of each function. Then graph one period of the function.
y = 4 cos(2x − π)
Problem 47
In Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 1/2 cos (3x + π/2)
Problem 49
In Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 cos (2x − π/2)
Problem 51
In Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 2 cos (2πx + 8π)
Problem 53
In Exercises 53–60, use a vertical shift to graph one period of the function. y = sin x + 2
Problem 56
In Exercises 53–60, use a vertical shift to graph one period of the function. y = cos x + 3
Problem 60
In Exercises 53–60, use a vertical shift to graph one period of the function. y = −3 sin 2πx + 2
Problem 62
In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = 3 cos x + sin x
Problem 64
In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = cos x + cos 2x