ArcTan
ArcTan[z]
gives the arc tangent of the complex number
.
ArcTan[x,y]
gives the arc tangent of , taking into account which quadrant the point
is in.
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- All results are given in radians.
- For real
, the results are always in the range
to
.
- For certain special arguments, ArcTan automatically evaluates to exact values.
- ArcTan can be evaluated to arbitrary numerical precision.
- ArcTan automatically threads over lists.
- ArcTan[z] has branch cut discontinuities in the complex
plane running from
to
and
to
.
- If
or
is complex, then ArcTan[x,y] gives
. When
, ArcTan[x,y] gives the number
such that
and
.
Background & Context
- ArcTan is the inverse tangent function. For a real number x, ArcTan[x] represents the radian angle measure
such that
. The two-argument form ArcTan[x,y] represents the arc tangent of y/x, taking into account the quadrant in which the point
lies. It therefore gives the angular position (expressed in radians) of the point measured from the positive
axis. ArcTan is consequently useful when converting from Cartesian to polar coordinate systems and for finding the phase
in phasor notation
.
- ArcTan automatically threads over lists. For certain special exact arguments, ArcTan automatically evaluates to exact values. When given exact numeric expressions as arguments, ArcTan may be evaluated to arbitrary numeric precision. Operations useful for manipulation of symbolic expressions involving ArcTan include FunctionExpand, TrigToExp, TrigExpand, Simplify, and FullSimplify.
- ArcTan is defined for complex argument
via
. ArcTan[z] has branch cut discontinuities in the complex
plane.
- Related mathematical functions include Arg, Tan, ArcCot, ArcTanh, and Gudermannian.
Examples
open allclose allBasic Examples (5)
Scope (6)
Generalizations & Extensions (3)
Applications (5)
Properties & Relations (7)
Possible Issues (1)
Neat Examples (1)
See Also
Arg Tan ArcCot ArcTanh Degree TrigToExp TrigExpand Gudermannian
Tutorials
Related Guides
Related Links
Introduced in 1988
(1.0)