^{-1}function is drawn on the x-axis across the same axis.

As the inverse tangent function is a multivalued function, we need a branch cut in the complex plane to resolve its values.

We can mathematically express the tan

^{-1}function as,

tan

^{-1}y = 1 / 2 i [ ln ( 1- i y) – ln ( 1 + i y ) ],here, ‘i’ represents for complex numbers. As we discussed the branch cut provides the range for tan

^{-1}function.

The range for x – axis along positive direction is,

Range = ( - ∏/2 , ∏/2 )

The most common range of tan

^{-1}in other quadrants is in the interval (∏ , 0 ).

There are some common values for the inverse tan function as,

tan

^{-1}( - i ) = - 1 ∞,

tan

^{-1}( - i ) = - i ∞,

tan

^{-1}0 = 0,

tan

^{-1}i = i ∞,

The differentiation of the inverse tan function is defined mathematically as:

d ( tan

^{-1}y ) / dy = 1 / ( 1+ y

^{2}).

Similarly, the Integration is obtained by the reverse process,

∫ tan

^{-1}y dy = y tan

^{-1}y – 1 / 2 lm ( 1 + y

^{2}) + k,

‘k’ is the integration constant.

In the form of complex numbers,

The inverse tan is,

∅=tan

^{-1}( y / x ),

Here, ∅is the angle measured in the clockwise direction.