The function f(x) = sin x
with domain
is not one - to - one.
However, f(x) = sin x with domain
is an increasing
one-to-one function that takes on every value in the range of the sine function, that is, every value
from -1 to 1.
Definition
.
The restricted sine function defined by
y = sin x,
with
and
has an inverse
y=sin -1x
or
y = arcsin x
with
and
.
The graph of
y = arcsin x
can be found by reflecting the graph
y = sin x
for
across the line y = x.
Table shows a partial numerical representation of
arcsin x