General solution: sin x = sin α (sin x = sin α ⟹ x = nπ + (−1)ⁿ α, n ∈ ℤ)

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sin x = sin α ⟹ x = nπ + (−1)ⁿ α, n ∈ ℤ

What each symbol means

SymbolWhat it stands for
nAny integer
αReference angle

When to use this

Covers all solutions. For sin x = 0: x = nπ. For sin x = 1: x = (4n+1)π/2.