Name        

Notation        

Domain

Range

 Inverse Sine

arcsin(x) or ${\sin }^{-1}\left(x\right)$

$\left|x\right| \le 1$

$\left[-\frac{\mathrm{\pi }}{2}\,\frac{\mathrm{\pi }}{2}\right]$

Inverse Cosine

arccos(x) or ${\cos }^{-1}\left(x\right)$

$\left|x\right| \le 1$

$\left[0\,\mathrm{\π}\right]$

Inverse Tangent

arctan(x) or ${\tan }^{-1}\left(x\right)$

$x \in \mathrm{\ℝ}$

$\left(-\frac{\mathrm{\pi }}{2}\,\frac{\mathrm{\pi }}{2}\right)$

Inverse Cosecant

arccsc(x) or ${\csc }^{-1}\left(x\right)$

$x\le -1 \mathbf{or} x\ge 1$

$\left[-\frac{\mathrm{\pi }}{2}\, 0\right) \mathbf{or} \left(0\,\frac{\mathrm{\π}}{2}\right]$

Inverse Secant

arcsec(x) or ${\sec }^{-1}\left(x\right)$

$x\le -1 \mathbf{or} x\ge 1$

$\left[0\,\frac{\mathrm{\π}}{2}\right) \mathbf{or} \left(\frac{\mathrm{\π}}{2}\,\mathrm{\π}\right]$

Inverse Cotangent

arccot(x) or ${\cot }^{-1}\left(x\right)$

$x \in \mathrm{\ℝ}$

$\left(0\,\mathrm{\pi }\right)$