Question
Find the set of values of:
\[ \csc^{-1}\left(\frac{\sqrt{3}}{2}\right) \]
Solution
We know the domain of inverse cosecant:
\[ |x| \ge 1 \]
But,
\[ \frac{\sqrt{3}}{2} < 1 \]
So, the value lies outside the domain.
Hence,
\[ \csc^{-1}\left(\frac{\sqrt{3}}{2}\right) \text{ is not defined in real numbers} \]
Final Answer:
\[ \boxed{\text{No real value (undefined)}} \]
Key Concept
Inverse cosecant exists only when \( |x| \ge 1 \). Values between −1 and 1 are not allowed.