Poll Results

Total votes: 950

Huh??: 266 (28.0%)
inverse hyperbolic sine of x: 199 (20.9%)
arc-sine-aitch of x: 61 (6.4%)
sine-aitch to the minus one of x: 58 (6.1%)
sine-aitch to the minus one x: 55 (5.8%)
inverse hyperbolic sine x: 52 (5.5%)
inverse sine-aitch of x: 46 (4.8%)
hyperbolic sine inverse of x: 33 (3.5%)
arc-sine-aitch x: 32 (3.4%)
arc-shine x: 29 (3.1%)
inverse shine x: 18 (1.9%)
sine-aitch inverse of x: 17 (1.8%)
inverse shine of x: 16 (1.7%)
arc-shine of x: 14 (1.5%)
inverse sine-aitch x: 13 (1.4%)
sine-aitch inverse x: 11 (1.2%)
shine to the minus one x: 10 (1.1%)
shine inverse x: 8 (0.8%)
shine to the minus one of x: 6 (0.6%)
hyperbolic sine inverse x: 5 (0.5%)
shine inverse of x: 3 (0.3%)

Okay, this poll proves that there are some questions for which I can't anticipate all the answers. Several people wrote to tell me (or hacked the voting form) to indicate some variant using the pronunciation "sinch". It was a dozen or more, but I didn't keep careful count so didn't include them in the results. Apparently this is a relatively common pronunciation in the United States, but I'd never even heard of it.

Also, a few Europeans wrote to tell me they use a pronunciation something like "arcsinus hyperbolicus", based on Latin.

And for those who answered "Huh??", the hyperbolic sine function is used in fields such as engineering, physics, and other egghead subjects. (Also, that Wikipedia article indicates two common pronunciations for "sinh", which I obviously didn't look at when I wrote the poll question.)