ArcTanDegrees [z]
gives the arc tangent in degrees of the complex number .
ArcTanDegrees
ArcTanDegrees [z]
gives the arc tangent in degrees of the complex number .
Details
- ArcTanDegrees , along with other inverse trigonometric and trigonometric functions, is studied in high-school geometry courses and is also used in many scientific disciplines.
- All results are given in degrees.
- For real , the results are always in the range to .
- ArcTanDegrees [z] returns the angle in degrees for which the ratio of the opposite side to the adjacent side of a right triangle is .
- For certain special arguments, ArcTanDegrees automatically evaluates to exact values.
- ArcTanDegrees can be evaluated to arbitrary numerical precision.
- ArcTanDegrees automatically threads over lists.
- ArcTanDegrees [z] has branch cut discontinuities in the complex plane running from to and to .
- ArcTanDegrees can be used with Interval , CenteredInterval and Around objects.
- Mathematical function, suitable for both symbolic and numerical manipulation.
Examples
open all close allBasic Examples (7)
Results are in degrees:
Calculate the angle BAC of this right triangle:
Calculate by hand:
The numerical value of this angle:
Solve an inverse trigonometric equation:
Solve an inverse trigonometric inequality:
Apply ArcTanDegrees to the following list:
Plot over a subset of the reals:
Series expansion at 0:
Scope (40)
Numerical Evaluation (6)
Evaluate numerically:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate ArcTanDegrees efficiently at high precision:
Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:
Or compute average-case statistical intervals using Around :
Compute the elementwise values of an array:
Or compute the matrix ArcTanDegrees function using MatrixFunction :
Specific Values (5)
Values of ArcTanDegrees at fixed points:
Simple exact values are generated automatically:
Values at infinity:
Zero of ArcTanDegrees :
Find the value of satisfying equation :
Substitute in the value:
Visualize the result:
Visualization (4)
Plot the ArcTanDegrees function:
Plot over a subset of the complexes:
Plot the real part of ArcTanDegrees :
Plot the imaginary part of ArcTanDegrees :
Polar plot with ArcTanDegrees :
Function Properties (12)
ArcTanDegrees is defined for all real values:
Complex domain:
ArcTanDegrees achieves all real values from the interval :
The range for complex values:
ArcTanDegrees is an odd function:
ArcTanDegrees has the mirror property tan^(-1)(TemplateBox[{x}, Conjugate])=TemplateBox[{{{tan, ^, {(, {-, 1}, )}}, (, x, )}}, Conjugate]:
ArcTanDegrees is an analytic function of over the reals:
It is neither analytic nor meromorphic over the complex plane:
ArcTanDegrees is an increasing function:
ArcTanDegrees is injective:
ArcTanDegrees is not surjective:
ArcTanDegrees is neither non-negative nor non-positive:
ArcTanDegrees has no singularities or discontinuities:
ArcTanDegrees is neither convex nor concave:
ArcSind is convex for x in [-10,0]:
TraditionalForm formatting:
Differentiation (3)
First derivative:
Higher derivatives:
Formula for the ^(th) derivative:
Integration (2)
Indefinite integral of ArcTanDegrees :
Definite integral of ArcTanDegrees over an interval centered at the origin is 0:
Series Expansions (5)
Taylor expansion for ArcTanDegrees :
Plot the first three approximations for ArcTanDegrees around :
Asymptotic expansions at Infinity :
Asymptotic expansion at one of the singular points:
Find series expansions at branch points and branch cuts:
ArcTanDegrees can be applied to a power series:
Function Identities and Simplifications (2)
Use FullSimplify to simplify expressions with ArcTanDegrees :
Use TrigToExp to express ArcTanDegrees using Log :
Function Representations (1)
Represent using ArcCotDegrees :
Applications (7)
Solve inverse trigonometric equations:
Solve an inverse trigonometric equation with a parameter:
Use Reduce to solve inequalities involving ArcTanDegrees :
Numerically find a root of a transcendental equation:
Plot the function to check if the solution is correct:
Plot the real and imaginary parts of ArcTanDegrees :
Different combinations of ArcTanDegrees with trigonometric functions:
Addition theorem for tangent function:
Properties & Relations (5)
Compositions with the inverse trigonometric functions:
Use PowerExpand to disregard multivaluedness of the ArcTanDegrees :
Alternatively, evaluate under additional assumptions:
Branch cuts of ArcTanDegrees run along the imaginary axis:
ArcTanDegrees gives the angle in degrees, while ArcTan gives the same angle in radians:
FunctionExpand applied to ArcTanDegrees generates expressions in trigonometric functions in radians:
ExpToTrig applied to the outputs of TrigToExp will generate trigonometric functions in radians:
Possible Issues (1)
Generically :
This differs from the original argument by a factor of :
Neat Examples (2)
Solve trigonometric equations involving ArcTanDegrees :
Numerical value of this angle in degrees:
Plot ArcTanDegrees at integer points:
See Also
Tech Notes
Related Guides
History
Text
Wolfram Research (2024), ArcTanDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcTanDegrees.html.
CMS
Wolfram Language. 2024. "ArcTanDegrees." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArcTanDegrees.html.
APA
Wolfram Language. (2024). ArcTanDegrees. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcTanDegrees.html
BibTeX
@misc{reference.wolfram_2025_arctandegrees, author="Wolfram Research", title="{ArcTanDegrees}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ArcTanDegrees.html}", note=[Accessed: 11-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_arctandegrees, organization={Wolfram Research}, title={ArcTanDegrees}, year={2024}, url={https://reference.wolfram.com/language/ref/ArcTanDegrees.html}, note=[Accessed: 11-January-2026]}