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문제 67
Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = sec⁻¹ (―1.2871684)
문제 73
Graph each inverse circular function by hand.
y = arcsec [(1/2)x]
문제 75
Evaluate each expression without using a calculator.
tan (arccos 3/4)
문제 77
Evaluate each expression without using a calculator.
cos (tan⁻¹ (-2))
문제 79
Evaluate each expression without using a calculator.
sin (2 tan⁻¹ (12/5))
문제 81
Evaluate each expression without using a calculator.
cos (2 arctan (4/3))
문제 83
Evaluate each expression without using a calculator.
sin (2 cos⁻¹ (1/5))
문제 85
Evaluate each expression without using a calculator.
sec (sec⁻¹ 2)
문제 87
Evaluate each expression without using a calculator.
cos (tan⁻¹ (5/12) - tan⁻¹ (3/4))
문제 89
Evaluate each expression without using a calculator.
sin (sin⁻¹ 1/2 + tan⁻¹ (-3))
문제 91
Use a calculator to find each value. Give answers as real numbers.
cos (tan⁻¹ 0.5)
문제 93
Use a calculator to find each value. Give answers as real numbers.
tan (arcsin 0.12251014)
문제 95
Write each trigonometric expression as an algebraic expression in u, for u > 0.
sin (arccos u)
문제 97
Write each trigonometric expression as an algebraic expression in u, for u > 0.
cos (arcsin u)
문제 99
Write each trigonometric expression as an algebraic expression in u, for u > 0.
sin (2 sec⁻¹ u/2)
문제 101
Write each trigonometric expression as an algebraic expression in u, for u > 0.
tan (sin⁻¹ u/(√u² + 2))
문제 103
Write each trigonometric expression as an algebraic expression in u, for u > 0.
sec (arccot (√4―u² )/ u)
문제 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°).
<IMAGE>
cos x = 1/2
문제 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°).
<IMAGE>
cos x = √3/2
문제 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°).
<IMAGE>
sin x = ―1/2
문제 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°).
<IMAGE>
sin x = ―√3/2
문제 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
문제 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
문제 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
문제 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
문제 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
문제 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
문제 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
문제 6.2.41
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
tan² θ + 4 tan θ + 2 = 0
문제 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