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Lean-Workbook Plus 43176: Trigonometric identity

Proved
WorkbookRestored.plus_43176

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For every m∈[−1,1]m\in[-1,1]m∈[−1,1], there is θ∈[−π/2,π/2]\theta\in[-\pi/2,\pi/2]θ∈[−π/2,π/2] such that m=sin⁡θm=\sin\thetam=sinθ.

Source: Lean-Workbook row lean_workbook_plus_43176 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
open Real
Formal statement
theorem WorkbookRestored.plus_43176 : ∀ m : ℝ, m ∈ Set.Icc (-1) 1 → ∃ θ : ℝ, θ ∈ Set.Icc (-Real.pi/2) (Real.pi/2) ∧ m = Real.sin θ   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_43176; immutable original Prove2Me node 31c8b9e4-0023-4969-b7c4-94e79a6bfc95

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