Trigonometry
      Inverse Trigonometric Functions or Arc-functions and their Graphs
         Inverse functions
      The arc-sine function and the arc-cosine function
         The arc-sine function
         The arc-cosine function
         The graph of the arc-sine function and the arc-cosine function
Inverse Trigonometric Functions or Arc-functions and their Graphs
Inverse functions
The inverse function, usually written  f -1, is the function whose domain and the range are respectively the range and domain of a given function f, that is
f -1(x) = y  if and only if ƒ (y) = x .
Thus, the composition of the inverse function and the given function returns x, which is called the identity function, i.e.,
f -1(ƒ(x)) = x    and    ƒ (f -1(x)) = x.
The inverse of a function undoes the procedure (or function) of the given function.
A pair of inverse functions is in inverse relation.
Example:  If given ƒ (x) = log2 x  then  f -1(x)  = 2x  since,
   
The arc-sine function and the arc-cosine function
  -  The arc-sine function  y = sin-1x or  y = arcsin x is the inverse of the sine function, so that its value for any argument is an arc (angle) whose sine equals the given argument.
That is,  y = sin-1x if and only if  x = sin y.  For example,
Thus, the arc-sine function is defined for arguments between -1 and 1, and its principal values are by convention taken to be those between -p/2 and p/2.
  -  The arc-cosine function  y = cos-1x or  y = arccos x is the inverse of the cosine function, so that its value for any argument is an arc (angle) whose cosine equals the given argument.
That is,  y = cos-1x if and only if  x = cos y.  For example,
Thus, the arc-cosine function is defined for arguments between -1 and 1, and its principal values are by convention taken to be those between 0 and p.
The graph of the arc-sine function and the arc-cosine function
Trigonometry contents B
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