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Problem 6.5
Find the exact value of each real number y. Do not use a calculator.
y = sin⁻¹ √2/2
Problem 6.51
The following equations cannot be solved by algebraic methods. Use a graphing calculator to find all solutions over the interval [0, 6]. Express solutions to four decimal places.
(arctan x)³ ― x + 2 = 0
Problem 6.51
Use a calculator to approximate each value in decimal degrees.
θ = arccos (-0.39876459)
Problem 6.53
Use a calculator to approximate each value in decimal degrees.
θ = csc⁻¹ 1.9422833
Problem 6.55
Use a calculator to approximate each value in decimal degrees.
θ = cot⁻¹ (-0.60724226)
Problem 6.55
Solve each equation for x.
4/3 arctan x/2 = π
Problem 6.57
Solve each equation for x.
arccos x + arctan 1 = 11π/12
Problem 6.57
Use a calculator to approximate each value in decimal degrees.
θ = tan⁻¹ (-7.7828641)
Problem 6.59
Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = arcsin 0.92837781
Problem 6.61
Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = cos⁻¹ (―0.32647891)
Problem 6.61
Solve each equation for x.
y = 1/2 tan (3x + 2), for x in [-2/3 - π/6, -2/3 + π/6]
Problem 6.63
Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = arctan 1.1111111
Problem 6.65
Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = cot⁻¹ (―0.92170128)
Problem 6.67
Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = sec⁻¹ (―1.2871684)
Problem 6.7
Solve each equation for x, where x is restricted to the given interval.
y = 5 cos x , for x in [0, π]
Problem 6.7
Find the exact value of each real number y. Do not use a calculator.
y = tan⁻¹ (―√3)
Problem 6.73
Graph each inverse circular function by hand.
y = arcsec [(1/2)x]
Problem 6.75
Evaluate each expression without using a calculator.
tan (arccos 3/4)
Problem 6.77
Evaluate each expression without using a calculator.
cos (tan⁻¹ (-2))
Problem 6.79
Evaluate each expression without using a calculator.
sin (2 tan⁻¹ (12/5))
Problem 6.81
Evaluate each expression without using a calculator.
cos (2 arctan (4/3))
Problem 6.83
Evaluate each expression without using a calculator.
sin (2 cos⁻¹ (1/5))
Problem 6.85
Evaluate each expression without using a calculator.
sec (sec⁻¹ 2)
Problem 6.87
Evaluate each expression without using a calculator.
cos (tan⁻¹ (5/12) - tan⁻¹ (3/4))
Problem 6.89
Evaluate each expression without using a calculator.
sin (sin⁻¹ 1/2 + tan⁻¹ (-3))
Problem 6.9
Solve each equation for x, where x is restricted to the given interval.
y = 3 tan 2x , for x in [―π/4, π/4]
Problem 6.9
Find the exact value of each real number y. Do not use a calculator.
y = cos⁻¹ (―√2/2)
Problem 6.91
Use a calculator to find each value. Give answers as real numbers.
cos (tan⁻¹ 0.5)
Problem 6.93
Use a calculator to find each value. Give answers as real numbers.
tan (arcsin 0.12251014)
Problem 6.95
Write each trigonometric expression as an algebraic expression in u, for u > 0.
sin (arccos u)