Inverse trigonometry

When we write \sin^{-1}x, for example, it is ambiguous. Do we mean:

We can be more clear using this terminology:

Inverse functionReciprocol function
\sin x[[arc]]\sin xcosec x
\cos x[[arc]]\cos xsec x
\tan x[[arc]]\tan xcot x

flashcards

QuestionAnswer
What is the ambiguity when writing \sin^{-1}x?It could mean either the principle value for which \sin \theta = x or the inverse function of \sin x (\frac{1}{\sin x}).
What is the clearer terminology for the inverse function of \sin x?\arcsin x
What is the clearer terminology for the reciprocal function of \sin x?\csc x (cosec x)
What is the clearer terminology for the inverse function of \cos x?\arccos x
What is the reciprocal function of \cos x?\sec x
What is the clearer terminology for the inverse function of \tan x?\arctan x
What is the reciprocal function of \tan x?\cot x