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Csc

Status: Stable

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

Description

Csc[z]
    gives the cosecant of z (= 1 / Sin[z]).
Csc is Listable. Singularities at z = k Pi yield ComplexInfinity.

Examples

No verified examples yet for this function.

Implementation notes

Algorithm. builtin_csc (src/trig.c) applies: (1) strip_inverse_call folds Csc[ArcCsc[x]] -> x. (2) odd_fold for oddness Csc[-x] -> -Csc[x]. (3) trig_i_fold rewrites Csc[I y] -> -I Csch[y]. (4) Csc[0] -> ComplexInfinity. (5) For a rational multiple of Pi (extract_pi_multiplier), exact_csc returns the closed-form surd from the table for denominators 1,2,3,4,5,6,10,12. (6) Numeric fallback: MPFR via mpfr_csc/mpfr_complex_csc, else get_approx + 1/csin(c) for inexact inputs. Otherwise NULL. (Unlike Cos/Tan, Csc has no forward-of-inverse fold step.)

Data structures. Expr* trees via the make_* helpers; Pi multiples as int64_t n, d.

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]:= Csc[Pi/6]
Out[1]= 2

In[1]:= Csc[Pi/12]
Out[1]= Sqrt[2] (1 + Sqrt[3])

In[1]:= N[Csc[1], 40]
Out[1]= 1.1883951057781212162615994523745510035279

In[1]:= Series[Csc[x], {x, 0, 5}]
Out[1]= 1/x + 1/6 x + 7/360 x^3 + 31/15120 x^5 + O[x]^6

In[1]:= Csc[I]
Out[1]= -I Csch[1]

Notes

Csc[z] is 1/Sin[z]. Singularities at z = k Pi yield ComplexInfinity. Csc is Listable. Exact special angles are returned in closed radical form, the Laurent expansion gives the cosecant's pole at the origin, and imaginary arguments map onto the hyperbolic cosecant.