The notation is sometimes also used (Gellert et al. 1989, p. 222; Gradshteyn and Ryzhik 2000, p. xxix). Note that the cosecant does not appear to be in consistent widespread use in Europe, although it does appear explicitly in various German and Russian handbooks (e.g., Gellert et al. 1989, p. 222; Gradshteyn and Ryzhik 2000, pp. xxix and p. 43). Interestingly, while is treated on par with the other trigonometric functions in some tabulations (Gellert et al. 1989, p. 222), it is not in others (Gradshteyn and Ryzhik 2000, who do not list it in their table of "basic functional relations" on p. 28, but do give identities involving it on p. 43).
Harris and Stocker (1998, p. 300) call secant and cosecant "rarely used functions," but then devote an entire section to them. Because these functions do seem to be in widespread use in the United States (e.g., Abramowitz and Stegun 1972, p. 72), reports of their demise seem to be a bit premature.
The positive integer values of giving incrementally largest values of are given by 1, 3, 22, 333, 355, 103993, ... (OEIS A046947), which are precisely the numerators of the convergents of and correspond to the values 1.1884, 7.08617, 112.978, 113.364, 33173.7, ....
is the function defined by 
is the sine. The cosecant is implemented in the Wolfram Language as Csc[z]. 
is sometimes also used (Gellert et al. 1989, p. 222; Gradshteyn and Ryzhik 2000, p. xxix). Note that the cosecant does not appear to be in consistent widespread use in Europe, although it does appear explicitly in various German and Russian handbooks (e.g., Gellert et al. 1989, p. 222; Gradshteyn and Ryzhik 2000, pp. xxix and p. 43). Interestingly, while 
is treated on par with the other trigonometric functions in some tabulations (Gellert et al. 1989, p. 222), it is not in others (Gradshteyn and Ryzhik 2000, who do not list it in their table of "basic functional relations" on p. 28, but do give identities involving it on p. 43). 
![intcsczdz=ln[sin(1/2z)]-ln[cos(1/2z)]+C,](https://mathworld.wolfram.com/images/equations/Cosecant/NumberedEquation2.svg)
is a constant of integration. For 
on the real axis, this simplifies to 
![ln[tan(1/2z)]+C](https://mathworld.wolfram.com/images/equations/Cosecant/Inline15.svg)
is a Bernoulli number. 
giving incrementally largest values of 
are given by 1, 3, 22, 333, 355, 103993, ... (OEIS A046947), which are precisely the numerators of the convergents of 
and correspond to the values 1.1884, 7.08617, 112.978, 113.364, 33173.7, .... 
and Cosecant 
Functions." Ch. 33 in