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20.1 The Inverse Sine Defined by: x=sin y

20.1.1 Graphs

This function, sometimes called arcsine, is denoted by sin-1 or arcsinx.

Since sine takes on the same value at x and x + 2p, you must restrict the range of arcsin x to make it a well defined function. It is standard to define arcsine to lie between - p / 2 and p / 2. Since holds, arcsin x is only defined for .

Arcsin x is a tame looking function, except that its derivative is infinite at .

Recalling that the derivative of a function is the reciprocal of the derivative of its inverse at corresponding points, we observe that this last statement corresponds to the fact that


20.1.2 The derivative of inverse sine