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Problem 29
Solve each equation for exact solutions.
6 sin⁻¹ x = 5π
Problem 31
Solve each equation for exact solutions.
cos⁻¹ x = sin⁻¹ 3/5
Problem 33
Solve each equation for exact solutions.
tan⁻¹ x = cot⁻¹ 7/5
Problem 35
Solve each equation for exact solutions.
arcsin x = arctan 3/4
Problem 37
Solve each equation for exact solutions.
2 arccos (x/3 - π/3) = 2π
Problem 39
Solve each equation for exact solutions.
sin⁻¹ x - tan⁻¹ 1 = -π/4
Problem 41
Solve each equation for exact solutions.
arccos x + 2 arcsin √3/2 = π
Problem 43
Solve each equation for exact solutions.
sin⁻¹ x - 4 tan⁻¹ (-1) = 2π
Problem 45
Solve each equation for exact solutions.
arcsin 2x + arccos x = π/6
Problem 47
Solve each equation for exact solutions.
cos⁻¹ x + tan⁻¹ x = π/2
Problem 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 57
Solve each equation for x.
arccos x + arctan 1 = 11π/12
Problem 5
Find the exact value of each real number y. Do not use a calculator.
y = sin⁻¹ √2/2
Problem 6.RE.45
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth of a degree, as appropriate.
sin² θ + 3 sin θ + 2 = 0
Problem 6.RE.41
Solve each equation over the interval [0, 2π). Write solutions as exact values or to four decimal places, as appropriate.
tan² 2x -1 = 0
Problem 6.RE.47
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth of a degree, as appropriate.
sin 2θ = cos 2θ +1
Problem 6.RE.37
Solve each equation over the interval [0, 2π). Write solutions as exact values or to four decimal places, as appropriate.
2 tan x -1 = 0
Problem 6.RE.39
Solve each equation over the interval [0, 2π). Write solutions as exact values or to four decimal places, as appropriate.
tan x = cot x
Problem 6.RE.49
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth of a degree, as appropriate.
3 cos² θ + 2 cos θ - 1 = 0
Problem 6.RE.43
Solve each equation for all exact solutions, in radians.
cos 2x + cos x = 0
Problem 7
Find the exact value of each real number y. Do not use a calculator.
y = tan⁻¹ (―√3)
Problem 11
Find the exact value of each real number y. Do not use a calculator.
y = sec⁻¹ (―2)
Problem 13
Find the exact value of each real number y. Do not use a calculator.
y = arccot (―1)
Problem 15
Give the degree measure of θ. Do not use a calculator.
θ = arcsin (―√3/2)
Problem 17
Use a calculator to approximate each value in decimal degrees.
θ = arctan 1.7804675
Problem 19
Use a calculator to approximate each value in decimal degrees.
θ = cos⁻¹ 0.80396577
Problem 21
Use a calculator to approximate each value in decimal degrees.
θ = arcsec 3.4723155
Problem 23
Evaluate each expression without using a calculator.
cos (arccos (-1))
Problem 25
Evaluate each expression without using a calculator.
arccos (cos (3π/4))
Problem 27
Evaluate each expression without using a calculator.
tan⁻¹ (tan (π/4))