ArcSinDegrees
gives the arc sine in degrees of the complex number .
Details
- ArcSinDegrees, 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 .
- ArcSinDegrees[z] returns the angle in degrees for which the ratio of the opposite side to the hypotenuse of a right triangle is .
- For certain special arguments, ArcSinDegrees automatically evaluates to exact values.
- ArcSinDegrees can be evaluated to arbitrary numerical precision.
- ArcSinDegrees automatically threads over lists.
- ArcSinDegrees[z] has branch cut discontinuities in the complex plane running from to and to .
- ArcSinDegrees can be used with Interval, CenteredInterval and Around objects.
- Mathematical function, suitable for both symbolic and numerical manipulation.
Examples
open allclose allBasic Examples (7)
Calculate the angle ABC of this right triangle:
The numerical value of this angle:
Solve an inverse trigonometric equation:
Solve an inverse trigonometric inequality:
Apply ArcSinDegrees to the following list:
Scope (39)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
ArcSinDegrees can take complex number inputs:
Evaluate ArcSinDegrees 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 ArcSinDegrees function using MatrixFunction:
Specific Values (5)
Values of ArcSinDegrees at fixed points:
Simple exact values are generated automatically:
Zero of ArcSinDegrees:
Visualization (4)
Plot the ArcSinDegrees function:
Plot over a subset of the complexes:
Plot the real part of ArcSinDegrees:
Plot the imaginary part of ArcSinDegrees:
Polar plot with ArcSinDegrees:
Function Properties (11)
ArcSinDegrees is defined for all real values from the interval :
Complex domain is the whole plane:
ArcSinDegrees achieves all real values from the interval :
ArcSinDegrees is an odd function:
ArcSinDegrees is not an analytic function:
ArcSinDegrees is neither non-decreasing nor non-increasing:
It is monotonic over its real domain:
ArcSinDegrees is injective:
ArcSinDegrees is not surjective:
ArcSinDegrees is neither non-negative nor non-positive:
ArcSinDegrees has both singularity and discontinuity in (-∞,-1] and [1,∞):
ArcSinDegrees is neither convex nor concave:
ArcSinDegrees is concave for x in [-1,0]:
TraditionalForm formatting:
Integration (2)
Indefinite integral of ArcSinDegrees:
Definite integral of ArcSinDegrees over an interval centered at the origin is 0:
Series Expansions (5)
Find the Taylor expansion using Series:
Plot the first three approximations for ArcSinDegrees around :
Asymptotic expansion at Infinity:
Asymptotic expansion at a singular point:
Find series expansions at branch points and branch cuts:
ArcSinDegrees can be applied to power series:
Function Identities and Simplifications (2)
Simplify expressions involving ArcSinDegrees:
Use TrigToExp to express through logarithms and square roots:
Function Representations (1)
Represent using ArcCscDegrees:
Applications (9)
Solve an inverse trigonometric equation:
Solve an inverse trigonometric equation with a parameter:
Get the zeros of ArcSinDegrees:
Use Reduce to solve inequalities involving ArcSinDegrees:
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 ArcSinDegrees:
Plot the Riemann surface of ArcSinDegrees:
Find the angle between two 3D vectors:
Different combinations of ArcSinDegrees with trigonometric functions:
Properties & Relations (5)
Compositions with the inverse trigonometric functions:
Use PowerExpand to disregard multivaluedness of the ArcSinDegrees:
Alternatively, evaluate under additional assumptions:
This shows the branch cuts of the ArcSinDegrees function:
ArcSinDegrees gives the angle in degrees, while ArcSin gives the same angle in radians:
FunctionExpand applied to ArcSinDegrees generates expressions in trigonometric functions in radians:
ExpToTrig applied to the outputs of TrigToExp will generate trigonometric functions in radians:
Possible Issues (3)
Neat Examples (3)
Solve trigonometric equations involving ArcSinDegrees:
Numerical value of this angle in degrees:
Calculate numerical values of ArcSinDegrees by iteration:
Plot ArcSinDegrees at integer points:
Text
Wolfram Research (2024), ArcSinDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcSinDegrees.html.
CMS
Wolfram Language. 2024. "ArcSinDegrees." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArcSinDegrees.html.
APA
Wolfram Language. (2024). ArcSinDegrees. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcSinDegrees.html