what is the range of y = csc⁻¹(x)?\n-\\frac{\\pi}{2},\\frac{\\pi}{2}\n-\\frac{\\pi}{2},0) and…

what is the range of y = csc⁻¹(x)?\n-\\frac{\\pi}{2},\\frac{\\pi}{2}\n-\\frac{\\pi}{2},0) and (0,\\frac{\\pi}{2}\n0,\\pi\n0,\\frac{\\pi}{2}) and (\\frac{\\pi}{2},\\pi\ndone

what is the range of y = csc⁻¹(x)?\n-\\frac{\\pi}{2},\\frac{\\pi}{2}\n-\\frac{\\pi}{2},0) and (0,\\frac{\\pi}{2}\n0,\\pi\n0,\\frac{\\pi}{2}) and (\\frac{\\pi}{2},\\pi\ndone

Answer

Brief Explanations:

The inverse - cosecant function (y = \csc^{-1}(x)) is the inverse of the cosecant function. The range of (y=\csc^{-1}(x)) is defined such that (y\in\left[-\frac{\pi}{2},0\right)\cup\left(0,\frac{\pi}{2}\right]). This is because the cosecant function (y = \csc(x)=\frac{1}{\sin(x)}), and when we define its inverse, we restrict the domain of the sine function (since (\csc(x)) is related to (\sin(x))) to (\left[-\frac{\pi}{2},0\right)\cup\left(0,\frac{\pi}{2}\right]) to make it one - to - one.

Answer:

(\left[-\frac{\pi}{2},0\right)\text{ and }\left(0,\frac{\pi}{2}\right])