How do you do simplify ${csc}^{- 1} (- \frac{2 \sqrt{3}}{3})$ $csc^-1 (-(2sqrt3)/3)$ ?

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How do you do simplify ${csc}^{- 1} (- \frac{2 \sqrt{3}}{3})$ $csc^-1 (-(2sqrt3)/3)$ ?

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Answer 1 · 2016-02-15T04:39:27

$- \frac{π}{3}, - \frac{2 π}{3}$ $-pi/3, -(2pi)/3$

Explanation:

$csc x = \frac{1}{sin x}$ $csc x = 1/sin x$
$csc x = (\frac{- 2 \sqrt{3}}{3})$ $csc x = ((-2sqrt3)/3)$ --> $sin x = (- \frac{3}{2 \sqrt{3}}) = - \frac{\sqrt{3}}{2}$ $sin x = (-3/(2sqrt3)) = -sqrt3/2$

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

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How do you do simplify ${csc}^{- 1} (- \frac{2 \sqrt{3}}{3})$ $csc^-1 (-(2sqrt3)/3)$ ?

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How do you do simplify ${csc}^{- 1} (- \frac{2 \sqrt{3}}{3})$ $csc^-1 (-(2sqrt3)/3)$ ?