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.

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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 The domain of the inverse sine function is . The range of the inverse sine function is . The inverse sine function is increasing. The inverse sine function is an odd, that is, arcsin(-x) = -arcsin x . arcsin(sin x) = x for . sin(arcsin x) = x for .

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