204
III - Convergence: Continuous variables
Example 3. It is "well known" that the function sin x is continuous and
strictly increasing on the interval [-rr /2, rr /2]; it therefore maps this interval
onto the interval [-1,1]' whence arises the possibility of defining the continuous map
arcsin x : [-1,1]----+ [-rr/2,rr/2].
The same method allows one to define the functions
arccos x
arctan x
[-1,1]
IR
----+ [0, rr],
----+ ]- rr/2,rr/2[.
III - Convergence: Continuous variables
Example 3. It is "well known" that the function sin x is continuous and
strictly increasing on the interval [-rr /2, rr /2]; it therefore maps this interval
onto the interval [-1,1]' whence arises the possibility of defining the continuous map
arcsin x : [-1,1]----+ [-rr/2,rr/2].
The same method allows one to define the functions
arccos x
arctan x
[-1,1]
IR
----+ [0, rr],
----+ ]- rr/2,rr/2[.