Blitzer - Trigonometry 3rd Edition - Chapter 2

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

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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 2.27

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function.

y = 3 sin(πx + 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 18

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function.

y = sin (x − π/2)

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 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 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 26

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.

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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