方程 cos(x) = m 有解当且仅当 -1 ≤ m ≤ 1

α = ±α₀ + 2πn

(其中 n ∈ ℤ)

💡 为什么是 ±?

因为 cos(-α) = cos(α) —— 余弦是偶函数!

求解:cos(2x) = ½

解答:

1. 条件:½ ∈ [-1,1] ✓

2. 基本解:cos(π/3) = ½,所以 α₀ = π/3

3. 通解:

2x = π/3 + 2πn → x = π/6 + πn

2x = -π/3 + 2πn → x = -π/6 + πn