How do you do simplify $csc^-1 (-(2sqrt3)/3)$ ?

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Answer 1 · 2016-02-15T04:39:27

$-pi/3, -(2pi)/3$

$csc x = 1/sin x$
$csc x = ((-2sqrt3)/3)$ --> $sin x = (-3/(2sqrt3)) = -sqrt3/2$

Unit circle and trig table of special arcs give:
$sin x = - sqrt3/2$ --> arc $x = -pi/3$ and $x = -(2pi)/3$ .

How do you do simplify csc^-1 (-(2sqrt3)/3)csc^-1 (-(2sqrt3)/3)?