




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