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 39–54, find the exact value of each expression, if possible. Do not use a calculator. tan⁻¹ [tan(− π/6)]
Problem 47
- In Exercises 29–51, find the exact value of each expression. Do not use a calculator. tan [cos⁻¹ (− 4/5)]
Problem 47
- In Exercises 45–52, graph two periods of each function. y = sec(2x + π/2) − 1
Problem 47
- In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. tan⁻¹ (tan 2π/3)
Problem 49
- In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin⁻¹(sin π/3)
Problem 49
- In Exercises 45–52, graph two periods of each function. y = csc|x|
Problem 49
- In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. sin⁻¹ (sin π)
Problem 51
- In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin⁻¹(cos 2π/3)
Problem 51
- In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. sin(sin⁻¹ π)
Problem 53
- In Exercises 53–54, let f(x) = 2 sec x, g(x) = −2 tan x, and h(x) = 2x − π/2. Graph two periods of y = (f∘h)(x).
Problem 53
- In Exercises 53–60, use a vertical shift to graph one period of the function. y = sin x + 2
Problem 53
- In Exercises 52–53, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. sec(sin⁻¹ 1/x)
Problem 53
- In Exercises 55–62, use the properties of inverse functions f(f⁻¹ (x)) = x for all x in the domain of f⁻¹ and f⁻¹(f(x)) for all x in the domain of f, as well as the definitions of the inverse cotangent, cosecant, and secant functions, to find the exact value of each expression, if possible. cot(cot⁻¹ 9π)
Problem 55
- In Exercises 53–60, use a vertical shift to graph one period of the function. y = cos x + 3
Problem 56
- In Exercises 55–62, use the properties of inverse functions f(f⁻¹ (x)) = x for all x in the domain of f⁻¹ and f⁻¹(f(x)) for all x in the domain of f, as well as the definitions of the inverse cotangent, cosecant, and secant functions, to find the exact value of each expression, if possible. sec(sec⁻¹ 7π)
Problem 57
- In Exercises 55–62, use the properties of inverse functions f(f⁻¹ (x)) = x for all x in the domain of f⁻¹ and f⁻¹(f(x)) for all x in the domain of f, as well as the definitions of the inverse cotangent, cosecant, and secant functions, to find the exact value of each expression, if possible. cot⁻¹ (cot 3π/4)
Problem 59
- In Exercises 53–60, use a vertical shift to graph one period of the function. y = −3 sin 2πx + 2
Problem 60
- 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 62
- In Exercises 63–82, use a sketch to find the exact value of each expression. cos (sin⁻¹ 4/5)
Problem 63
- In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = cos x + cos 2x
Problem 64
- In Exercises 63–82, use a sketch to find the exact value of each expression. tan (cos⁻¹ 5/13)
Problem 65
- In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = cos x + sin 2x
Problem 66
- In Exercises 63–82, use a sketch to find the exact value of each expression. tan [sin⁻¹ (− 3/5)]
Problem 67
- In Exercises 67–68, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 4. y = cos πx + sin π/2 x
Problem 68
- In Exercises 63–82, use a sketch to find the exact value of each expression. _ sin (cos⁻¹ √2/2)
Problem 69
- In Exercises 63–82, use a sketch to find the exact value of each expression. tan [cos⁻¹ (− 1/3)]
Problem 73
- In Exercises 63–82, use a sketch to find the exact value of each expression. cos [tan⁻¹ (− 2/3)]
Problem 77
- In Exercises 63–82, use a sketch to find the exact value of each expression. cot (csc⁻¹ 8)
Problem 80
- In Exercises 79–82, graph f, g, and h in the same rectangular coordinate system for 0 ≤ x ≤ 2π. Obtain the graph of h by adding or subtracting the corresponding y-coordinates on the graphs of f and g. f(x) = 2 cos x, g(x) = cos 2x, h(x) = (f + g)(x)
Problem 80
- In Exercises 79–82, graph f, g, and h in the same rectangular coordinate system for 0 ≤ x ≤ 2π. Obtain the graph of h by adding or subtracting the corresponding y-coordinates on the graphs of f and g. f(x) = cos x, g(x) = sin 2x, h(x) = (f − g)(x)
Problem 82