The ancient mathematician Native American Sohcahtoa had distant Asiatic cousin, whose name was Choshacao. Although, he was less well known (and probably made up in my Functions, Statistics, and Trigonometry class many years ago), his name helps us relate the inverse trigonometric properties.

CHO: Cosecant = Hypotenuse / Opposite
SHA: Secant = Hypotenuse / Adjacent
CAO: Cotangent = Adjacent / Opposite

This mnemonic doesn't work as well, since it repeats the letter "C" for two words.