Skip to content

Tan

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Tan[z]
    gives the tangent of z. Equivalent to Sin[z] / Cos[z].
Tan is Listable. Singularities at z = Pi/2 + k Pi yield ComplexInfinity.

Examples

No verified examples yet for this function.

Implementation notes

Algorithm. builtin_tan mirrors the Sin cascade in src/trig.c: strip_inverse_call(arg, "ArcTan") for Tan[ArcTan[x]] -> x; try_simp_forward_of_inverse for Tan of the other inverse trig functions (Tan[ArcSin[x]] -> x/Sqrt[1-x^2], Tan[ArcCos[x]] -> Sqrt[1-x^2]/x, Tan[ArcCot[x]] -> 1/x); odd_fold for the odd symmetry Tan[-x] -> -Tan[x]; trig_i_fold for Tan[I y] -> I Tanh[y]; and Tan[0] = 0. Exact rational-multiple-of-Pi values are detected by extract_pi_multiplier and computed by exact_tan (a denominator-switch table analogous to exact_sin).

Numeric. MPFR-valued arguments go through numeric_mpfr_apply_unary(..., mpfr_tan) with an mpfr_complex_tan complex fallback; otherwise get_approx plus ctan produces a machine-precision real or Complex result, only when the argument is inexact. Symbolic arguments return NULL. Attributes: ATTR_LISTABLE | ATTR_NUMERICFUNCTION | ATTR_PROTECTED.

Attributes: Listable, NumericFunction, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= Tan[Pi/4]
Out[1]= 1

In[2]:= N[Tan[1]]
Out[2]= 1.55741

In[3]:= Tan[Pi/2]
Out[3]= ComplexInfinity

In[1]:= Tan[Pi/12]
Out[1]= 2 - Sqrt[3]

In[1]:= N[Tan[1], 40]
Out[1]= 1.5574077246549022305069748074583601730872

In[1]:= Simplify[Tan[ArcSin[x]]]
Out[1]= x/Sqrt[1 - x^2]

Notes

Tan[z] is equivalent to Sin[z]/Cos[z]. Singularities at z = Pi/2 + k Pi yield ComplexInfinity. Tan is Listable.