Trigonometric equations and standard transformations - One Line Questions
1.
What is the principal value of arcsin(-1/2)? —
-π/6
2.
Find the value of cos(105°). —
(√2 - √6) / 4
3.
What is the value of sin(15°)? —
(√6 - √2) / 4
4.
The value of cos(75°) is: —
(√6 - √2) / 4
5.
The value of sin(105°) is: —
(√6 + √2) / 4
6.
How many solutions does the equation sin x = 1/2 have in the interval [0, 2π]? —
2
7.
The number of solutions of the equation sin x = x/10 in the interval [-π, π] is: —
3
8.
What is the value of tan(15°)? —
2 - √3
9.
What is the value of tan(75°)? —
2 + √3
10.
If tan(x + y) = 1 and tan(x - y) = 1/2, then tan(2x) is equal to: —
3/2
11.
The general solution of the equation 2 sin^2 x + sin x - 1 = 0 is: —
nπ + (-1)^n (-π/6), n ∈ Z
12.
Solve for x: 2 cos^2 x + 3 sin x = 0. —
nπ + (-1)^n (-π/6), n ∈ Z
13.
If sin x = 1/√2, then x is equal to: —
nπ + (-1)^n π/4, n ∈ Z
14.
Solve for x: sin(2x) = cos(x). —
nπ/3, n ∈ Z
15.
The general solution of cos x = -1 is: —
x = (2n + 1)π, where n ∈ Z
16.
If sin x = cos y, then the general solution is: —
x = (2n + 1)π/2 - y, n ∈ Z
17.
The general solution of sin x + cos x = 0 is: —
x = (2n + 1)π/4, where n ∈ Z
18.
Find the general solution of sin x = -1. —
x = 2nπ - π/2, where n ∈ Z
19.
Find the general solution of sin x = 1. —
x = 2nπ + π/2, where n ∈ Z
20.
The general solution of sin(x/2) = 1/2 is: —
x = 4nπ + 2π/3, where n ∈ Z
21.
Find the general solution of cos x = -1/2. —
x = 2nπ ± 2π/3, where n ∈ Z
22.
If cos x = cos α, then the general solution is: —
x = 2nπ ± α, where n ∈ Z
23.
The general solution of cos x = 1/2 is: —
x = 2nπ ± π/3, where n ∈ Z
24.
The equation cos x = √3/2 has the general solution: —
x = 2nπ ± π/6, where n ∈ Z
25.
The general solution of cos x = 1 is: —
x = 2nπ, where n ∈ Z
26.
Find the general solution of cos(2x) = cos(x). —
x = 2nπ/3 or x = 2nπ, n ∈ Z
27.
Find the general solution of tan(2x) = tan(x/2). —
x = 2nπ/5, where n ∈ Z
28.
The general solution of tan(x/4) = 1 is: —
x = 4nπ + π/4, where n ∈ Z
29.
Find the general solution of cos(x/3) = √3/2. —
x = 6nπ ± π/6, where n ∈ Z
30.
What is the general solution for tan x = -1? —
x = nπ - π/4, where n ∈ Z
31.
The general solution of tan x = -1/√3 is: —
x = nπ - π/6, where n ∈ Z
32.
The general solution of sin x = -√3/2 is: —
x = nπ + (-1)^n (-π/3), n ∈ Z
33.
If sin x = sin α, then the general solution is: —
x = nπ + (-1)^n α, where n ∈ Z
34.
Solve for x: sin(2x) = sin(π/3). —
x = nπ/2 + (-1)^n π/6, n ∈ Z
35.
If tan x = sin(π/4) / cos(π/3), then the general solution is: —
x = nπ + arctan(√2 / 2), n ∈ Z
36.
If tan x = tan α, then the general solution is: —
x = nπ + α, where n ∈ Z
37.
Solve for x: tan x = √3. —
x = nπ + π/3, where n ∈ Z
38.
What is the general solution for tan x = 1? —
x = nπ + π/4, where n ∈ Z
39.
The general solution of cos(2x) = cos(π/4) is: —
x = nπ ± π/8, where n ∈ Z
40.
The general solution of sin(2x) = sin(x) is: —
x = nπ or x = 2nπ ± π/3, n ∈ Z
41.
What is the general solution of the equation sin x = 0? —
x = nπ, where n ∈ Z
42.
The general solution of cos x = 0 is: —
x = (2n + 1)π/2, where n ∈ Z
43.
What is the general solution for tan x = 0? —
x = nπ, where n ∈ Z
44.
Find the general solution of cos 2x = cos^2 x. —
x = nπ, where n ∈ Z
45.
The general solution of tan(2x) = tan(x) is: —
x = nπ, where n ∈ Z
46.
If sin(3x) = sin(x), then the general solution is: —
x = nπ/2 or x = 2nπ ± π/3, n ∈ Z
47.
Solve for x: cos(3x) = cos(x). —
x = nπ/2 or x = nπ, n ∈ Z
48.
The general solution of tan(3x) = tan(x) is: —
x = nπ/2, where n ∈ Z
49.
The general solution of tan 3x = cot x is: —
x = nπ/4, where n ∈ Z
50.
Find the principal value of arccos(1/2). —
π/3