ArcCosDegrees [z]
gives the arc cosine in degrees of the complex number .
ArcCosDegrees
ArcCosDegrees [z]
gives the arc cosine in degrees of the complex number .
Details
- ArcCosDegrees , 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 between and , the results are always in the range to .
- ArcCosDegrees [z] returns the angle in degrees for which the ratio of the adjacent side to the hypotenuse of a right triangle is .
- For certain special arguments, ArcCosDegrees automatically evaluates to exact values.
- ArcCosDegrees can be evaluated to arbitrary numerical precision.
- ArcCosDegrees automatically threads over lists.
- ArcCosDegrees [z] has branch cut discontinuities in the complex plane running from to and to .
- ArcCosDegrees 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 ArcCosDegrees to the following list:
Plot over a subset of the reals:
Series expansion at 0:
Scope (38)
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 ArcCosDegrees 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 ArcCosDegrees function using MatrixFunction :
Specific Values (5)
Values of ArcCosDegrees at fixed points:
Simple exact values are generated automatically:
Values at infinity:
Zero of ArcCosDegrees :
Find the value of satisfying equation :
Substitute in the value:
Visualize the result:
Visualization (4)
Plot the ArcCosDegrees function:
Plot over a subset of the complexes:
Plot the real part of ArcCosDegrees :
Plot the imaginary part of ArcCosDegrees :
Polar plot with ArcCosDegrees :
Function Properties (10)
ArcCosDegrees is defined for all real values from the interval :
Complex domain is the whole plane:
ArcCosDegrees achieves all real values from the interval :
The range for complex values:
ArcCosDegrees is not an analytic function:
Nor is it meromorphic:
ArcCosDegrees is neither non-decreasing nor non-increasing:
It is monotonic over its real domain:
ArcCosDegrees is injective:
ArcCosDegrees is not surjective:
ArcCosDegrees is non-negative over its real domain:
ArcCosDegrees has both singularity and discontinuity in (-∞,-1] and [1,∞):
ArcCosDegrees is neither convex nor concave:
ArcCosDegrees is convex for x in [-1,0]:
TraditionalForm formatting:
Differentiation (3)
First derivative:
Higher derivatives:
Formula for the ^(th) derivative:
Integration (2)
Indefinite integral of ArcCosDegrees :
Definite integral of ArcCosDegrees over the entire real domain:
Series Expansions (5)
Find the Taylor expansion using Series :
Plot the first three approximations for ArcCosDegrees around :
Asymptotic expansion at Infinity :
Asymptotic expansion at a singular point:
Find the series expansion at branch points and branch cuts:
ArcCosDegrees can be applied to power series:
Function Identities and Simplifications (2)
Simplify expressions involving ArcCosDegrees :
Use TrigToExp to express through logarithms and square roots:
Function Representations (1)
Represent using ArcSecDegrees :
Applications (8)
Solve an inverse trigonometric equation:
Solve an inverse trigonometric equation with a parameter:
Get the zeros of ArcCosDegrees :
Use Reduce to solve inequalities involving ArcCosDegrees :
Numerically find a root of a transcendental equation:
Plot the function to check if the solution is correct:
Plot the real and imaginary part of ArcCosDegrees :
Plot the Riemann surface of ArcCosDegrees :
Find the angle between two vectors:
Properties & Relations (5)
Compose with the inverse function:
Use PowerExpand to disregard multivaluedness of the ArcCosDegrees :
Alternatively, evaluate under additional assumptions:
This shows the branch cuts of the ArcCosDegrees function:
ArcCosDegrees gives the angle in degrees, while ArcCos gives the same angle in radians:
FunctionExpand applied to ArcCosDegrees generates expressions in trigonometric functions in radians:
ExpToTrig applied to the outputs of TrigToExp will generate trigonometric functions in radians:
Possible Issues (3)
Generically :
On branch cuts, machine-precision inputs can give numerically wrong answers:
The precision of the output can be much less than the precision of the input:
Neat Examples (3)
Solve trigonometric equations involving ArcCosDegrees :
Numerical value of this angle in degrees:
Plot a specific ArcCosDegrees :
Plot ArcCosDegrees at integer points:
See Also
Tech Notes
Related Guides
History
Text
Wolfram Research (2024), ArcCosDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcCosDegrees.html.
CMS
Wolfram Language. 2024. "ArcCosDegrees." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArcCosDegrees.html.
APA
Wolfram Language. (2024). ArcCosDegrees. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcCosDegrees.html
BibTeX
@misc{reference.wolfram_2025_arccosdegrees, author="Wolfram Research", title="{ArcCosDegrees}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ArcCosDegrees.html}", note=[Accessed: 14-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_arccosdegrees, organization={Wolfram Research}, title={ArcCosDegrees}, year={2024}, url={https://reference.wolfram.com/language/ref/ArcCosDegrees.html}, note=[Accessed: 14-December-2025]}