Inverse Trigonometric Differentiation

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Unlike the six basic trigonometric functions, the six inverse trigonometric functions must have restricted domains. The reason being that the six basic trigonometric functions are periodic and as a result have no on-to-one inverses. Of coarse, all Calculus students should know the frase if and only if. This page will denote the frase as iff.

Inverse Trigonometric Functions

Function	Domain	Range
y = arcsin x iff sin y = x	-1 < x < 1	-pi/2 < y < pi/2
y = arccos x iff cos y = x	-1 < x < 1	0 < y < pi
y = arctan x iff tan y = x	-infinity < x < infinity	-pi/2 < y < pi/2
y = arccot x iff cot y = x	-infinity < x < infinity	0 < y < pi
y = arcsec x iff sec y = x	| x | > 1	0 < y < pi, y doesn't = 0
y = arccsc x iff csc y = x	| x | > 1	-pi/2 < y < pi/2, y doesn't = 0