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here is y = cos^-1x = arccosx and its graph:
open this image:
http://img23.imageshack.us/f/arccos3.gif/
Since {y = cos^-1(x) is the
of the function
, the function y = cos^-1(x)
and
.
But, since
is
, its
must be restricted in order that y = cos^-1(x) is a function.
To get the graph of y = cos^-1x, start with a graph of
.
the
of the function to a one-to-one region - typically [
,
] is used for cos^ -1x. This leaves the range of the restricted function unchanged as [
,
].
Reflect the graph across the line
to get the graph of y = cos^-1 x y = arccos x, the black curve at right on the graph above.
Notice that y = cos^-1x has domain [
,
] and range [
,
]. It is strictly decreasing on its entire domain.
