What is the principal value of sin⁻¹(1)?
A
0
B
π/2
C
π
D
1
Analysis & Theory
The principal value of sin⁻¹(1) is π/2.
What is the domain of the function sin⁻¹(x)?
A
(−∞, ∞)
B
[0, π]
C
[−1, 1]
D
[−π/2, π/2]
Analysis & Theory
sin⁻¹(x) is defined only for x ∈ [−1, 1].
What is the range of cos⁻¹(x)?
A
[0, π]
B
[−π/2, π/2]
C
[−1, 1]
D
[0, ∞)
Analysis & Theory
The range of cos⁻¹(x) is [0, π].
What is the value of tan⁻¹(0)?
A
0
B
π/2
C
1
D
Undefined
Analysis & Theory
tan⁻¹(0) = 0 is a standard inverse trigonometric value.
Which of the following is equal to sin⁻¹(−x)?
A
−sin⁻¹(x)
B
sin⁻¹(x)
C
cos⁻¹(x)
D
−cos⁻¹(x)
Analysis & Theory
sin⁻¹(−x) = −sin⁻¹(x); it's an odd function.
What is the principal value of cos⁻¹(1)?
A
π
B
π/2
C
0
D
1
Analysis & Theory
cos⁻¹(1) = 0 as 0 is in the principal value range [0, π].
Which of the following identities is true?
A
sin⁻¹(x) + cos⁻¹(x) = π/2
B
tan⁻¹(x) + cot⁻¹(x) = π
C
sec⁻¹(x) = 1/cos⁻¹(x)
D
cos⁻¹(x) = 1/sec⁻¹(x)
Analysis & Theory
sin⁻¹(x) + cos⁻¹(x) = π/2 is a standard identity.
The range of tan⁻¹(x) is:
A
[0, π]
B
(−π/2, π/2)
C
(−∞, ∞)
D
[−1, 1]
Analysis & Theory
The principal value branch for tan⁻¹(x) is (−π/2, π/2).
What is the value of sin⁻¹(0)?
A
π
B
0
C
π/2
D
1
Analysis & Theory
sin⁻¹(0) = 0.
Which of the following is not a valid expression?
A
cos⁻¹(2)
B
sin⁻¹(1/2)
C
tan⁻¹(1)
D
cot⁻¹(0)
Analysis & Theory
cos⁻¹(x) is only defined for x ∈ [−1, 1]; cos⁻¹(2) is invalid.