Inverse trigonometric functions and their properties - One Line Questions
1.
The domain of arcsin(x) is: —
[-1, 1]
2.
The domain of arccos(x) is: —
[-1, 1]
3.
The domain of arctan(x) is: —
(-∞, ∞)
4.
The principal value of arccot(x) lies in the interval: —
(0, π)
5.
What is the domain of the inverse trigonometric function arctan(x)? —
(-∞, ∞)
6.
The principal value range of arctan(x) is: —
(-π/2, π/2)
7.
The range of arccsc(x) is: —
[-π/2, 0) U (0, π/2]
8.
What is the principal value range of the inverse trigonometric function arcsin(x)? —
[-π/2, π/2]
9.
The principal value range of arccos(x) is: —
[0, π]
10.
The range of arcsec(x) is: —
[0, π/2) U (π/2, π]
11.
The value of arccos(0) is: —
π/2
12.
What is the value of cos(arctan(x))? —
1 / √(1 + x²)
13.
What is the value of sin(arccos(5/13))? —
12/13
14.
What is the value of sin(2 arctan(3/4))? —
24/25
15.
What is the value of arcsin(sin(2π/3))? —
π/3
16.
What is the value of tan(2 arctan(1/3))? —
3/4
17.
What is the value of tan(arcsin(3/5))? —
3/4
18.
What is the value of cos(2 arctan(1/2))? —
3/5
19.
What is the value of arccos(cos(4π/3))? —
2π/3
20.
What is the value of arctan(tan(5π/4))? —
π/4
21.
The value of 2arcsin(x) is equal to: —
arcsin(2x√(1-x²))
22.
The value of 2arccos(x) is equal to: —
arccos(2x² - 1)
23.
The value of arccos(12/13) + arccos(4/5) is: —
arccos(33/65)
24.
What is the value of arccos(x) + arccos(y)? —
arccos(xy - √(1-x²)√(1-y²))
25.
What is the value of arccos(x) - arccos(y)? —
arccos(xy + √(1-x²)√(1-y²))
26.
What is the relationship between arccot(x) and arctan(x)? —
arccot(x) + arctan(x) = π/2
27.
The value of arcsin(1/3) + arcsin(4/5) is: —
arcsin(63/65)
28.
Which property relates arcsin(x) and arccos(x)? —
arcsin(x) + arccos(x) = π/2
29.
What is the value of arcsin(x) - arcsin(y)? —
arcsin(x√(1-y²) - y√(1-x²))
30.
What is the value of arcsin(x) + arcsin(y)? —
arcsin(x√(1-y²) + y√(1-x²))
31.
The expression arctan(x) + arctan(y) is equal to: —
arctan((x+y)/(1-xy))
32.
The expression arctan(x) - arctan(y) is equal to: —
arctan((x-y)/(1+xy))
33.
The expression cot⁻¹(x) is equal to: —
tan⁻¹(1/x) for x > 0, π + tan⁻¹(1/x) for x < 0
34.
What is the value of tan(arctan(x))? —
x
35.
What is the value of sin(arcsin(x))? —
x
36.
What is the value of cos(arccos(x))? —
x
37.
What is the value of tan(arcsin(x))? —
x / √(1 - x²)
38.
The property 2arctan(x) = -π + arctan(2x / (1 - x^2)) is valid when: —
x < -1
39.
The property 2arctan(x) = arctan(2x / (1 - x^2)) is valid when: —
x < 1
40.
The property 2arctan(x) = π + arctan(2x / (1 - x^2)) is valid when: —
x > 1
41.
If tan⁻¹(x) + tan⁻¹(y) = π/2, then: —
xy = -1
42.
What is the value of arctan(1) + arctan(2) + arctan(3)? —
π
43.
Evaluate arcsin(-1). —
-π/2
44.
What is the value of arctan(0)? —
0
45.
If x > 0, then sin⁻¹(x) + cos⁻¹(x) = ? —
π/2
46.
If x < 0, then sin⁻¹(x) + cos⁻¹(x) = ? —
π/2
47.
Find the value of arccos(-1/2). —
2π/3
48.
What is the value of arccot(1)? —
π/4
49.
What is the value of arcsin(1/2)? —
π/6
50.
What is the value of arctan(√3)? —
π/3