SOLUTION: Please help... Sketch the graph of Arccos x if Cos x has a domain of 0 ≤ x ≤ π

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Question 439239: Please help...
Sketch the graph of Arccos x if Cos x has a domain of 0 ≤ x ≤ π
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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 inverse of the function y+=+cos+x, the function y = cos^-1(x)if and only+if+cos+y+=+x.
But, since y+=+cos+x is not one-to-one, its domain 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 y+=+cos+x.


Solved by pluggable solver: PLOT any graph
Graphing function cos%28x%29:

graph%28+500%2C+500%2C+-4%2C+4%2C+-4%2C+4%2C+cos%28x%29+%29


Restrict the domain of the function to a one-to-one region - typically [0, pi] is used for cos^ -1x. This leaves the range of the restricted function unchanged as [-1, 1].


Reflect the graph across the line y+=+x 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 [-1,+1] and range [0, pi]. It is strictly decreasing on its entire domain.