Question

domain and range of arccosecant

Answer 1

\[\cos(\frac{1}{\cos(\theta)})^{-1}\]
secant goes \[ I=[-1,0) \cup (0,1]\]
therefore the domain is everything except what makes cos=0, therefore
domain = \[J=\mathbb{R}-k\pi/2, \forall k \in \mathbb{N}\]