Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions
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Blitzer 3rd EditionCh. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions
Blitzer 3rd EditionCh. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions- 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 1
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)
- 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 3
- 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 5
- In Exercises 1–26, find the exact value of each expression. _ cos⁻¹ √3/2
Problem 7
- 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 9
- 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 13
- 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 15
- 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 17
Problem 18
Determine the amplitude, period, and phase shift of each function. Then graph one period of the function.
y = sin (x − π/2)
- In Exercises 1–26, find the exact value of each expression. _ cot⁻¹ √3
Problem 19
- 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 21
- 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 23
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)
- 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 25
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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- 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
