Inverse and Hyperbolic Flags
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There is no single-key equivalent to the `calc-arcsin' function.
Instead, you must first press `I' (`calc-inverse') to set the "Inverse
Flag", then press `S' (`calc-sin').  The `I' key actually toggles the
Inverse Flag.  When this flag is set, the word `Inv' appears in the
mode line.

Likewise, the `H' key (`calc-hyperbolic') sets or clears the
Hyperbolic Flag, which transforms `calc-sin' into `calc-sinh'.  If
both of these flags are set at once, the effect will be
`calc-arcsinh'.  (The Hyperbolic flag is also used by some
non-trigonometric commands; for example `H L' computes a base-10,
instead of base-e, logarithm.)

Command names like `calc-arcsin' are provided for completeness, and
may be executed with `x' or `M-x'.  Their effect is simply to toggle
the Inverse and/or Hyperbolic flags and then execute the corresponding
base command (`calc-sin' in this case).

The Inverse and Hyperbolic flags apply only to the next Calculator
command, after which they are automatically cleared.  (They are also
cleared if the next keystroke is not a Calc command.)  Digits you type
after `I' or `H' (or `K') are treated as prefix arguments for the next
command, not as numeric entries.  The same is true of `C-u', but not
of the minus sign (`K -' means to subtract and keep arguments).

The third Calc prefix flag, `K' (keep-arguments), is discussed
elsewhere.  See Keep Arguments.