Blitzer - Trigonometry 3rd Edition - Chapter 2

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Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions

Blitzer 3rd Edition

Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions

Problem 1
In Exercises 1–6, 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 1
In Exercises 1–26, find the exact value of each expression. sin⁻¹ 1/2
Problem 3
In Exercises 1–6, 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 3
In Exercises 1–26, find the exact value of each expression. _ sin⁻¹ √2/2
Problem 5
Graph y = 1/2 sin x + cos x, 0 ≤ x ≤ 2π.
Problem 5
In Exercises 1–6, 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 5
In Exercises 1–26, find the exact value of each expression. sin⁻¹ (- 1/2)
Problem 7
In Exercises 1–26, find the exact value of each expression. _ cos⁻¹ √3/2
Problem 9
In Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function. y = 3 sin 1/2 x
Problem 9
In Exercises 1–26, find the exact value of each expression. _ cos⁻¹ (- √2/2)
Problem 13
In Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function. y = -3 sin 2πx
Problem 13
In Exercises 1–26, find the exact value of each expression. _ tan⁻¹ √3/3
Problem 13
In Exercises 12–13, use a vertical shift to graph one period of the function. y = 2 cos 1/3 x − 2
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 15
In Exercises 14–15, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = sin x + cos 1/2 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 17
In Exercises 1–26, find the exact value of each expression. _ tan⁻¹ (−√3)
Problem 19
In Exercises 1–26, find the exact value of each expression. _ cot⁻¹ √3
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 21
In Exercises 1–26, find the exact value of each expression. _ cot⁻¹ (−√3)
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 23
In Exercises 1–26, find the exact value of each expression. _ csc⁻¹ (− 2√3/3)
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 25
In Exercises 1–26, find the exact value of each expression. _ sec⁻¹ (−√2)
Problem 25
In Exercises 25–28, use each graph to obtain the graph of the corresponding reciprocal function, cosecant or secant. Give the equation of the function for the graph that you obtain.
Problem 27
In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. sin⁻¹ 0.3
Problem 27
In Exercises 25–28, use each graph to obtain the graph of the corresponding reciprocal function, cosecant or secant. Give the equation of the function for the graph that you obtain.
Problem 29
In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. sin⁻¹ (-0.32)
Problem 29
In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 3 csc x
Problem 31
In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. cos⁻¹ 3/8

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