Theorems · Definition · complex analysis
Real.tan
ℝ → ℝ
The real tangent function, defined as the real part of the complex tangent
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 100 results in Mathlib
- Foundations
- Depth 144 from the axioms, rests on 3,710 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Complex.ofRealproof · cited by 1,654
- Complex.reproof · cited by 882
- Complex.tanproof · cited by 77
Cited by102
Results whose statement or proof uses this declaration.
- Real.Angle.tan_coestatement and proof · cited by 19
- Real.tan_eq_sin_div_cosstatement and proof · cited by 15
- Real.tan_periodicstatement · cited by 14
- Real.tan_arctanstatement · cited by 11
- Real.tanOrderIsoproof · cited by 10
- Complex.ofReal_tanstatement · cited by 9
- Real.tan_zerostatement · cited by 8
- Real.arctan_addproof · cited by 6
- Real.hasDerivAt_tanstatement and proof · cited by 6
- InnerProductGeometry.tan_angle_add_of_inner_eq_zerostatement and proof · cited by 5
- Real.tan_negstatement · cited by 5
- Real.inv_one_add_tan_sqstatement and proof · cited by 4