Theorems · Theorem · real analysis
Complex.cos_sub_pi_div_two
∀ (x : ℂ), Complex.cos (x - ↑Real.pi / 2) = Complex.sin x
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- mul_negproof · cited by 590
- Complex.cosstatement and proof · cited by 279
- Complex.sinstatement and proof · cited by 258
- Complex.cos_negproof · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- Complex.sin_eq_zero_iffproof · cited by 3
- Complex.inv_Gammaℝ_two_subproof · cited by 2
- Complex.sin_eq_one_iffproof · cited by 1
- Complex.cos_pi_div_two_subproof · cited by 1