Question

What is inverse of $csc$?

Answer 1

Inverse of $csc$:

• Inverse of $csc$ is denoted by $cs{c}^{-1}$.
• The domain of the function $y={\csc }^{-1}x$ is $\left(-\infty ,-1\right)\cup \left(1,\infty \right)$.
• The range of the $y={\csc }^{-1}x$ is $\left[-\frac{\pi }{2},\frac{\pi }{2}\right]-\left\{0\right\}$.
• The relation between ${\sec }^{-1}x$ and ${\csc }^{-1}x$ is ${\sec }^{-1}x+{\csc }^{-1}x=\frac{\pi }{2}$.
• The graph of the function $y={\csc }^{-1}x$ is