Trigonometric functions and identities - One Line Questions
1.
What is the value of sin(15°)? —
(√6 - √2)/4
2.
What is the value of cos(75°)? —
(√6 - √2)/4
3.
The identity tan(A + B) is: —
(tanA + tanB) / (1 - tanAtanB)
4.
The range of the sine function is: —
[-1, 1]
5.
The range of the cosine function is: —
[-1, 1]
6.
The range of the tangent function is: —
(-∞, ∞)
7.
If cos(θ) = -1/2, and θ is in the second quadrant, what is sin(θ)? —
√3/2
8.
What is the value of tan(45°)? —
1
9.
The fundamental identity of trigonometry states that sin²(θ) + cos²(θ) is equal to: —
1
10.
What is the value of sin(90°)? —
1
11.
What is the value of cos(0°)? —
1
12.
What is the value of tan(0°)? —
0
13.
What is the value of sin(180°)? —
0
14.
What is the value of cos(180°)? —
-1
15.
What is the value of tan(180°)? —
0
16.
What is the value of sin(270°)? —
-1
17.
What is the value of cos(270°)? —
0
18.
What is the value of tan(270°)? —
Undefined
19.
What is the value of sin(360°)? —
0
20.
What is the value of cos(360°)? —
1
21.
What is the value of tan(360°)? —
0
22.
What is the value of tan(π/4) in radians? —
1
23.
If sin(θ) = -1, what is the principal value of θ? —
270°
24.
If cos(θ) = 1, what is the principal value of θ? —
0°
25.
If tan(θ) = 1, and θ is in the third quadrant, what is sin(θ)? —
-1/√2
26.
What is the value of sin(30°)? —
1/2
27.
What is the value of cos(60°)? —
1/2
28.
What is the value of sin(π/6) in radians? —
1/2
29.
What is the value of cos(π/3) in radians? —
1/2
30.
If tan(A) = 1/2 and tan(B) = 1/3, what is tan(A + B)? —
1
31.
If sin(θ) = 1/2, what are the possible values for θ in the range [0°, 360°)? —
30°, 150°
32.
What is the value of cos(3θ) in terms of cos(θ)? —
4cos³(θ) - 3cos(θ)
33.
What is the value of sin(3θ) in terms of sin(θ)? —
3sin(θ) - 4sin³(θ)
34.
If sin(θ) = 3/5, and θ is in the first quadrant, what is cos(θ)? —
4/5
35.
The identity cos(2θ) can be expressed in three forms. One of them is: —
cos(2θ) = 2cos²(θ) - 1
36.
Which quadrant is characterized by positive sine and negative cosine? —
Second
37.
If sin(θ) = sin(α), then the general solution for θ is: —
nπ + (-1)ⁿα
38.
If cos(θ) = cos(α), then the general solution for θ is: —
2nπ ± α
39.
If tan(θ) = tan(α), then the general solution for θ is: —
nπ + α
40.
The double angle formula for sine is: —
sin(2θ) = 2sin(θ)cos(θ)
41.
What is the value of sin(A)cos(B) + cos(A)sin(B)? —
sin(A + B)
42.
What is the value of cos(A)cos(B) - sin(A)sin(B)? —
cos(A - B)
43.
The identity 1 + tan²(θ) = sec²(θ) is derived from which fundamental identity? —
sin²(θ) + cos²(θ) = 1
44.
The identity 1 + cot²(θ) = cosec²(θ) is derived from which fundamental identity? —
sin²(θ) + cos²(θ) = 1
45.
The identity sin(A + B) is: —
sinAcosB + cosAsinB
46.
The identity cos(A - B) is: —
cosAcosB + sinAsinB
47.
Which trigonometric function has a value of 0 at 0° and 180°? —
Tangent
48.
What is the period of the sine function? —
2π
49.
What is the period of the cosine function? —
2π
50.
What is the period of the tangent function? —
π