The general solution of sin x = 0 is:
Analysis & Theory
sin x = 0 when x = 0, π, 2π, ... which is x = nπ, where n is an integer.
The general solution of cos x = 0 is:
Analysis & Theory
cos x = 0 when x = π/2, 3π/2, ... which is x = π/2 + nπ, n ∈ Z.
The general solution of tan x = 1 is:
Analysis & Theory
tan x = 1 at x = π/4, 5π/4, ... which is x = π/4 + nπ, n ∈ Z.
The general solution of sin x = 1/2 is:
A
x = π/6 + 2nπ or x = 5π/6 + 2nπ, n ∈ Z
Analysis & Theory
sin x = 1/2 at x = π/6 and 5π/6 in [0, 2π], general solution x = π/6 + 2nπ or x = 5π/6 + 2nπ.
The general solution of cos x = -1/2 is:
A
x = 2π/3 + 2nπ or x = 4π/3 + 2nπ, n ∈ Z
B
x = π/3 + 2nπ or x = 5π/3 + 2nπ, n ∈ Z
Analysis & Theory
cos x = -1/2 at x = 2π/3 and 4π/3 in [0, 2π], general solution x = 2π/3 + 2nπ or x = 4π/3 + 2nπ.
The general solution of tan x = √3 is:
Analysis & Theory
tan x = √3 at x = π/3, 4π/3, general solution x = π/3 + nπ.
The general solution of 2 sin x - 1 = 0 is:
A
x = π/6 + 2nπ or x = 5π/6 + 2nπ, n ∈ Z
Analysis & Theory
2 sin x - 1 = 0 ⇒ sin x = 1/2, so solution is x = π/6 + 2nπ or x = 5π/6 + 2nπ.
The general solution of 3 cos x + √3 = 0 is:
A
x = 5π/6 + 2nπ or x = 7π/6 + 2nπ, n ∈ Z
B
x = π/3 + 2nπ or x = 2π/3 + 2nπ, n ∈ Z
Analysis & Theory
3 cos x + √3 = 0 ⇒ cos x = -√3/3, solutions are x = 5π/6, 7π/6, general solution x = 5π/6 + 2nπ or x = 7π/6 + 2nπ.
The general solution of sin 2x = 0 is:
Analysis & Theory
sin 2x = 0 ⇒ 2x = nπ ⇒ x = nπ/2, n ∈ Z.
The general solution of cos 2x = 1/2 is:
A
x = π/6 + nπ or x = 5π/6 + nπ, n ∈ Z
B
x = π/3 + nπ or x = 2π/3 + nπ, n ∈ Z
Analysis & Theory
cos 2x = 1/2 ⇒ 2x = π/3 + 2nπ or 2x = 5π/3 + 2nπ ⇒ x = π/6 + nπ or x = 5π/6 + nπ.