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Problem 6.27
Evaluate each expression without using a calculator.
tan⁻¹ (tan (π/4))
Problem 6.29
Solve each equation for exact solutions.
6 sin⁻¹ x = 5π
Problem 6.29
Find the exact value of each real number y if it exists. Do not use a calculator.
y = csc⁻¹ (―2)
Problem 6.29
Evaluate each expression without using a calculator.
sin (arccos (3/4))
Problem 6.3
Which one of the following equations has solution 3π/4
a. arctan 1 = x
b. arcsin √2/2 = x
c. arccos (―√2 /2) = x
Problem 6.31
Solve each equation for exact solutions.
cos⁻¹ x = sin⁻¹ 3/5
Problem 6.31
Find the exact value of each real number y if it exists. Do not use a calculator.
y = arcsec (2√3)/3
Problem 6.31
Evaluate each expression without using a calculator.
cos (csc⁻¹ (-2))
Problem 6.33
Solve each equation for exact solutions.
tan⁻¹ x = cot⁻¹ 7/5
Problem 6.33
Find the exact value of each real number y if it exists. Do not use a calculator.
y = sec⁻¹ 1
Problem 6.33
Evaluate each expression without using a calculator.
tan (arcsin (3/5) + arccos (5/7))
Problem 6.35
Solve each equation for exact solutions.
arcsin x = arctan 3/4
Problem 6.35
Find the exact value of each real number y if it exists. Do not use a calculator.
y = csc⁻¹ √2/2
Problem 6.35
Write each trigonometric expression as an algebraic expression in u, for u > 0.
tan (arcsec (√1―u²) / u)
Problem 6.37
Solve each equation for exact solutions.
2 arccos (x/3 - π/3) = 2π
Problem 6.37
Find the degree measure of θ if it exists. Do not use a calculator.
θ = arctan (-1)
Problem 6.39
Solve each equation for exact solutions.
sin⁻¹ x - tan⁻¹ 1 = -π/4
Problem 6.39
Find the degree measure of θ if it exists. Do not use a calculator.
θ = arcsin (-√3/2)
Problem 6.4
The point (π/4, 1) lies on the graph of y = tan x. Therefore, the point _______ lies on the graph of y = tan⁻¹ x.
Problem 6.41
Solve each equation for exact solutions.
arccos x + 2 arcsin √3/2 = π
Problem 6.41
Find the degree measure of θ if it exists. Do not use a calculator.
θ = arccos (-1/2)
Problem 6.43
Solve each equation for exact solutions.
sin⁻¹ x - 4 tan⁻¹ (-1) = 2π
Problem 6.43
Find the degree measure of θ if it exists. Do not use a calculator.
θ = cot⁻¹ (-√3/3)
Problem 6.45
Solve each equation for exact solutions.
arcsin 2x + arccos x = π/6
Problem 6.45
Find the degree measure of θ if it exists. Do not use a calculator.
θ = csc⁻¹ (-2)
Problem 6.47
Solve each equation for exact solutions.
cos⁻¹ x + tan⁻¹ x = π/2
Problem 6.47
Find the degree measure of θ if it exists. Do not use a calculator.
θ = sin⁻¹ 2
Problem 6.49
Use a calculator to approximate each value in decimal degrees.
θ = sin⁻¹ (-0.13349122)
Problem 6.49
Solve each equation for exact solutions.
tan⁻¹ x - tan⁻¹ (1/x ) = π/6
Problem 6.5
Which one of the following equations has solution π?
a. arccos (―1) = x
b. arccos 1 = x
c. arcsin (―1) = x