Find the principal values of the following:

    3. \textup{cosec}^{-1}(2)

Answers (1)

Let us assume that \textup{cosec}^{-1}(2) = x, then we have;

Cosec\ x = 2, or 

Cosec( \frac{\pi}{6}) = 2  .

And we know the range of principal values is  [\frac{-\pi}{2},\frac{\pi}{2}] - \left \{ 0 \right \}.

Therefore the principal value of  \textup{cosec}^{-1}(2) is \frac{\pi}{6}.

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