Inverse Trigonometric Function of Reciprocal

Theorem

For all $x \in \R$ for which the expressions above are defined:

Arcsine of Reciprocal equals Arccosecant

$\map \arcsin {\dfrac 1 x} = \arccsc x$

Arccosecant of Reciprocal equals Arcsine

$\map \arccsc {\dfrac 1 x} = \arcsin x$

Arccosine of Reciprocal equals Arcsecant

$\map \arccos {\dfrac 1 x} = \arcsec x$

Arcsecant of Reciprocal equals Arccosine

$\map \arcsec {\dfrac 1 x} = \arccos x$

Arctangent of Reciprocal equals Arccotangent

$\map \arctan {\dfrac 1 x} = \arccot x$

Arccotangent of Reciprocal equals Arctangent

$\map \arccot {\dfrac 1 x} = \arctan x$