How do you get the exact value of ${csc}^{- 1} (2)$ $csc^-1 (2)$ ?

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How do you get the exact value of ${csc}^{- 1} (2)$ $csc^-1 (2)$ ?

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Answer 1 · 2015-08-08T20:06:49

${csc}^{- 1} (2) = \frac{π}{6}$ $csc^(-1)(2) = pi/6$ or $\frac{5 π}{6}$ $(5pi)/6$

Explanation:

${csc}^{- 1} (2)$ $csc^(-1)(2)$
$XXXX$ $color(white)("XXXX")$ $= {sin}^{- 1} (\frac{1}{2})$ $=sin^(-1)(1/2)$

$XXXX$ $color(white)("XXXX")$ $= arcsin (\frac{1}{2})$ $=arcsin(1/2)$

$arcsin (\frac{1}{2}) = θ$ $arcsin(1/2) = theta$ means $sin (θ) = \frac{1}{2}$ $sin(theta) = 1/2$

If $sin (θ) = \frac{1}{2}$ $sin(theta) = 1/2$ (within the range $θ \in [0, 2 π]$ $theta in [0,2pi]$ )
then
$XXXX$ $color(white)("XXXX")$ $θ = \frac{π}{6}$ $theta = pi/6$ $XXXX$ $color(white)("XXXX")$ or $XXXX$ $color(white)("XXXX")$ $θ = \frac{5 π}{6}$ $theta = (5pi)/6$
(This is one of the standard angles)

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How do you get the exact value of ${csc}^{- 1} (2)$ $csc^-1 (2)$ ?

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How do you get the exact value of ${csc}^{- 1} (2)$ $csc^-1 (2)$ ?