Step By Step Calculus » 6.4 - Inverse Trigonometric Functions

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Synopsis
Domain and Ranges of Inverse Trigonometric Functions: Inverse trigonometric functions are the inverses of trigonometric functions with restricted domains -- to make them one-to-one. The following table shows the domains and ranges of the inverse trigonometric functions.
\[ \newcommand{\T}{\rule{0pt}{2.6ex}} \newcommand{\B}{\rule[-1.5ex]{0pt}{0pt}} \begin{array}{|l|l|l|} \hline \text{Function} & \text{Domain} & \text{Range} \\ \hline \T \B \sin ^{-1}\text{ or }\arcsin & [-1,1] & [-\frac{\pi }{2},\frac{\pi }{2}] \\ \hline \T\B \cos ^{-1}\text{ or }\arccos & [-1,1] & [0,\pi ] \\ \hline \T\B \tan ^{-1}\text{ or }\arctan & \mathbb{R} & (-\frac{\pi }{2},\frac{\pi }{2}) \\ \hline \T \B \csc ^{-1} \textrm{ or arccsc}& (-\infty ,-1]\cup [1,\infty ) & [-\frac{\pi }{2},0)\cup (0,% \frac{\pi }{2}] \\ \hline \T\B\sec ^{-1} \textrm{ or arcsec}& (-\infty ,-1]\cup [1,\infty ) & [0,\frac{\pi }{2})\cup (\frac{% \pi }{2},\pi ] \\ \hline \T \B \cot ^{-1}\text{ } \textrm{ or arccot}& \mathbb{R} & [-\frac{\pi}{2},0)\cup(0,\frac{\pi}{2}] \\ \hline \end{array} \]