Theorems · Theorem · real analysis
Real.sin_add_pi_div_two
∀ (x : ℝ), Real.sin (x + Real.pi / 2) = Real.cos x
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- 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
- Real.cosstatement and proof · cited by 424
- Real.sinstatement and proof · cited by 389
- Real.sin_pi_div_twoproof · cited by 29
- Real.cos_pi_div_twoproof · cited by 26
- Real.sin_addproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Real.cos_pos_of_mem_Iooproof · cited by 14
- Real.cos_nonneg_of_mem_Iccproof · cited by 10
- EulerSine.integral_cos_pow_eqproof · cited by 2
- HurwitzZeta.hurwitzZetaOdd_neg_two_mul_natproof · cited by 0
- Real.Angle.sin_add_pi_div_twoproof · cited by 0