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Problem 4.33
Decide whether each statement is true or false. If false, explain why.
The tangent and secant functions are undefined for the same values.
Problem 6.1
Which one of the following equations has solution 0?
a. arctan 1 = x
b. arccos 0 = x
c. arcsin 0 = x
Problem 6.101
Write each trigonometric expression as an algebraic expression in u, for u > 0.
tan (sin⁻¹ u/(√u² + 2))
Problem 6.103
Write each trigonometric expression as an algebraic expression in u, for u > 0.
sec (arccot (√4―u² )/ u)
Problem 6.11
Solve each equation for x, where x is restricted to the given interval.
y = 6 cos x/4 , for x in [0, 4π]
Problem 6.11
Find the exact value of each real number y. Do not use a calculator.
y = sec⁻¹ (―2)
Problem 6.13
Solve each equation for x, where x is restricted to the given interval.
y = ― 2 cos 5x , for x in [0, π/5]
Problem 6.13
Find the exact value of each real number y if it exists. Do not use a calculator.
y = sin⁻¹ 0
Problem 6.13
Find the exact value of each real number y. Do not use a calculator.
y = arccot (―1)
Problem 6.14
Find the exact value of each real number y if it exists. Do not use a calculator.
y = sin⁻¹ (―1)
Problem 6.15
Solve each equation for x, where x is restricted to the given interval.
y = sin x ―2 , for x in [―π/2. π/2]
Problem 6.15
Find the exact value of each real number y if it exists. Do not use a calculator.
y = cos⁻¹ (―1)
Problem 6.15
Give the degree measure of θ. Do not use a calculator.
θ = arcsin (―√3/2)
Problem 6.17
Solve each equation for x, where x is restricted to the given interval.
y = ―4 + 2 sin x , for x in [―π/2. π/2]
Problem 6.17
Find the exact value of each real number y if it exists. Do not use a calculator.
y = tan⁻¹ 1
Problem 6.17
Use a calculator to approximate each value in decimal degrees.
θ = arctan 1.7804675
Problem 6.19
Solve each equation for x, where x is restricted to the given interval.
y = 1/2 cot 3 x , for x in [0, π/3]
Problem 6.19
Find the exact value of each real number y if it exists. Do not use a calculator.
y = arctan 0
Problem 6.19
Use a calculator to approximate each value in decimal degrees.
θ = cos⁻¹ 0.80396577
Problem 6.21
Solve each equation for x, where x is restricted to the given interval.
y = cos (x + 3) , for x in [―3, π―3]
Problem 6.21
Find the exact value of each real number y if it exists. Do not use a calculator.
y = arcsin (―√3/2)
Problem 6.21
Use a calculator to approximate each value in decimal degrees.
θ = arcsec 3.4723155
Problem 6.23
Solve each equation for x, where x is restricted to the given interval.
y = √2 + 3 sec 2x, for x in [0, π/4) ⋃ (π/4, π/2]
Problem 6.23
Find the exact value of each real number y if it exists. Do not use a calculator.
y = arccos (―√3/2)
Problem 6.23
Evaluate each expression without using a calculator.
cos (arccos (-1))
Problem 6.25
Solve each equation for exact solutions.
-4 arcsin x = π
Problem 6.25
Find the exact value of each real number y if it exists. Do not use a calculator.
y = sin⁻¹ √3
Problem 6.25
Evaluate each expression without using a calculator.
arccos (cos (3π/4))
Problem 6.27
Solve each equation for exact solutions.
4/3 cos⁻¹ x/4 = π
Problem 6.27
Find the exact value of each real number y if it exists. Do not use a calculator.
y = cot⁻¹ (―1)
