Trigonometry Inverse Trigonometric Functions
The Inverse Sine Function
   Concepts 1

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
x -1 0 1
arcsin x 0

Properties of the inverse sine function
  1. The domain of the inverse sine function is .
  2. The range of the inverse sine function is .
  3. The inverse sine function is increasing.
  4. The inverse sine function is an odd, that is,
    arcsin(-x) = -arcsin x .
  5. arcsin(sin x) = x   for .
  6. sin(arcsin x) = x   for .


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