Question

Which inverse trigonometric function has a range of $\left(0,\mathrm{\pi }\right)$ ?

Answer 1

Find the inverse trigonometry function that have range $\left(0,\mathrm{\pi }\right)$ :

Inverse Trigonometric function is the polar opposite of trigonometry. They're also referred to as arcus functions.
Given,
The range of an inverse trigonometric function is $\left(0,\mathrm{\pi }\right)$

The range of the following functions is known:

The inverse of the cosine is $\left(0,\mathrm{\pi }\right)$.

From $\left(-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)$ comes the ${\sin }^{-1}\left(X\right)$

From $\left(\frac{-\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)$comes the ${\tan }^{-1}\left(X\right)$

Hence, the inverse trigonometric function with range $\left(0,\mathrm{\pi }\right)$ is, ${\cos }^{-1}\left(x\right)$.