holds,
arcsin x is only defined for 
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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 
