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Problem 67
Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = sec⁻¹ (―1.2871684)
Problem 73
Graph each inverse circular function by hand.
y = arcsec [(1/2)x]
Problem 75
Evaluate each expression without using a calculator.
tan (arccos 3/4)
Problem 77
Evaluate each expression without using a calculator.
cos (tan⁻¹ (-2))
Problem 79
Evaluate each expression without using a calculator.
sin (2 tan⁻¹ (12/5))
Problem 81
Evaluate each expression without using a calculator.
cos (2 arctan (4/3))
Problem 83
Evaluate each expression without using a calculator.
sin (2 cos⁻¹ (1/5))
Problem 85
Evaluate each expression without using a calculator.
sec (sec⁻¹ 2)
Problem 87
Evaluate each expression without using a calculator.
cos (tan⁻¹ (5/12) - tan⁻¹ (3/4))
Problem 89
Evaluate each expression without using a calculator.
sin (sin⁻¹ 1/2 + tan⁻¹ (-3))
Problem 91
Use a calculator to find each value. Give answers as real numbers.
cos (tan⁻¹ 0.5)
Problem 93
Use a calculator to find each value. Give answers as real numbers.
tan (arcsin 0.12251014)
Problem 95
Write each trigonometric expression as an algebraic expression in u, for u > 0.
sin (arccos u)
Problem 97
Write each trigonometric expression as an algebraic expression in u, for u > 0.
cos (arcsin u)
Problem 99
Write each trigonometric expression as an algebraic expression in u, for u > 0.
sin (2 sec⁻¹ u/2)
Problem 101
Write each trigonometric expression as an algebraic expression in u, for u > 0.
tan (sin⁻¹ u/(√u² + 2))
Problem 103
Write each trigonometric expression as an algebraic expression in u, for u > 0.
sec (arccot (√4―u² )/ u)
Problem 1
Use the unit circle shown here to solve each simple trigonometric equation. If the variable is x, then solve over [0, 2π). If the variable is θ, then solve over [0°, 360°).
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cos x = 1/2
Problem 2
Use the unit circle shown here to solve each simple trigonometric equation. If the variable is x, then solve over [0, 2π). If the variable is θ, then solve over [0°, 360°).
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cos x = √3/2
Problem 3
Use the unit circle shown here to solve each simple trigonometric equation. If the variable is x, then solve over [0, 2π). If the variable is θ, then solve over [0°, 360°).
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sin x = ―1/2
Problem 4
Use the unit circle shown here to solve each simple trigonometric equation. If the variable is x, then solve over [0, 2π). If the variable is θ, then solve over [0°, 360°).
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sin x = ―√3/2
Problem 6.2.59
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
5 + 5 tan² θ = 6 sec θ
Problem 6.2.49
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
3 csc x― 2√3 = 0
Problem 6.2.39
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
9 sin² θ ― 6 sin² θ = 1
Problem 6.2.35
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
2 tan θ sin θ - tan θ = 0
Problem 6.2.51
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
6 sin² θ + sin θ = 1
Problem 6.2.45
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
cot θ + 2 csc θ = 3
Problem 6.2.37
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
sec² θ tan θ = 2 tan θ
Problem 6.2.57
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
sin x (3 sin x - 1) = 1
Problem 6.2.63
The following equations cannot be solved by algebraic methods. Use a graphing calculator to find all solutions over the interval [0, 2π). Express solutions to four decimal places.
x² + sin x - x³ - cos x = 0