Arccosine online calculator (acos)
You can calculate the arccosine of given numbers in degrees and radians as follows.
The acos word works as a command to calculate the arccosine values and all numbers are separated by a space. In the above example, the calculator calculates the arccosines of -1, 0.5, 0.7. The results are in degrees and radians.
The arccosine function is the inverse of cosine and the range of cosine function is $[-1,\ 1]$. So the domain of arccosine is $[-1,\ 1]$. Even if you input 999 as an argument in the form, the calculator skips it.
The range of arccos
Because the arccosine function is the inverse of cosine, the arccosine is a multivalued function. For instance, arccos(0) is $\frac{\pi}{2}$ and $\frac{3\pi}{2}$ and $\frac{5\pi}{2}$. So it's common to set the principal value to see arccos() as a single valued function.
The principal value of arccosine is $[0,\ \pi]$.
The arccos formula
\[ \textnormal{arccos}( -x ) = \pi - \textnormal{arccos}( x ) \\~\\ \textnormal{arccos}( x ) = \frac{\pi}{2} - \textnormal{arcsin}( x ) \]
\[ \textnormal{cos}( \textnormal{arccos}(x) ) = x \\~\\ \textnormal{sin}( \textnormal{arccos}(x) ) = \sqrt{ 1 - x^2 } \\~\\ \textnormal{tan}( \textnormal{arccos}(x) ) = \frac{ \sqrt{ 1 - x^2 } }{ x } \]
\[ \textnormal{arccos}\left( \dfrac{1}{x} \right) = \textnormal{arcsec}( x ) \]
\[ \textnormal{arccos}( x ) = \dfrac{1}{2} \ \textnormal{arccos}( 2x^2 - 1 ) \quad (0 \leq x \leq 1) \]