CscDegrees
CscDegrees[θ]
gives the cosecant of degrees.
Details
![](Files/CscDegrees.en/details_1.png)
- CscDegrees and other trigonometric functions are studied in high-school geometry courses and are also used in many scientific disciplines.
- The argument of CscDegrees is assumed to be in degrees.
- CscDegrees of angle
is the ratio of the adjacent side to the hypotenuse of a right triangle:
- CscDegrees is related to SinDegrees by the identity
.
- For certain special arguments, CscDegrees automatically evaluates to exact values.
- CscDegrees can be evaluated to arbitrary numerical precision.
- CscDegrees automatically threads over lists.
- CscDegrees can be used with Interval, CenteredInterval and Around objects.
- Mathematical function, suitable for both symbolic and numerical manipulation.
Examples
open allclose allBasic Examples (6)
The argument is given in radians:
Calculate CscDegrees of 45 Degree for a right triangle with unit sides:
Calculate the cosecant by hand:
Solve a trigonometric equation:
Scope (46)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate CscDegrees 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 CscDegrees function using MatrixFunction:
Specific Values (6)
Values of CscDegrees at fixed points:
CscDegrees has exact values at rational multiples of 30 degrees:
Simple exact values are generated automatically:
More complicated cases require explicit use of FunctionExpand:
Singular points of CscDegrees:
Local extrema of CscDegrees:
Find a local minimum of CscDegrees as the root of in the minimum's neighborhood:
Visualization (4)
Plot the CscDegrees function:
Plot over a subset of the complexes:
Plot the real part of CscDegrees:
Plot the imaginary part of CscDegrees:
Polar plot with CscDegrees:
Function Properties (13)
CscDegrees is a periodic function with a period of :
Check this with FunctionPeriod:
The real domain of CscDegrees:
CscDegrees achieves all real values except from the open interval :
CscDegrees is an odd function:
CscDegrees has the mirror property :
CscDegrees is not an analytic function:
CscDegrees is monotonic in a specific range:
CscDegrees is not injective:
CscDegrees is not surjective:
CscDegrees is neither non-negative nor non-positive:
It has both singularity and discontinuity when x is a multiple of 180:
It is convex for x in [0,180]:
TraditionalForm formatting:
Integration (3)
Compute the indefinite integral of CscDegrees via Integrate:
Definite integral of CscDegrees over a period is 0:
Series Expansions (3)
Find the Taylor expansion using Series:
Plot the first three approximations for CscDegrees around :
Asymptotic expansion at a singular point:
CscDegrees can be applied to power series:
Function Identities and Simplifications (5)
Double-angle formula using TrigExpand:
Convert sums to products using TrigFactor:
Function Representations (3)
Representation through SinDegrees:
Representation through CosDegrees:
Representations through CosDegrees and CotDegrees:
Applications (11)
Basic Trigonomometric Applications (2)
Given , find the CscDegrees of the angle
using the formula
:
Find the missing opposite side length of a right triangle with hypotenuse 5 given the angle is 30 degrees:
Trigonomometric Identities (3)
Calculate the CscDegrees value of 105 degrees using the sum and difference formulas:
Trigonomometric Equations (2)
Trigonomometric Inequalities (2)
Properties & Relations (13)
Check that 1 degree is radians:
Basic parity and periodicity properties of the cosecant function get automatically applied:
Simplify under assumptions on parameters:
Complicated expressions containing trigonometric functions do not automatically simplify:
Use FunctionExpand to express CscDegrees in terms of radicals:
Compositions with the inverse trigonometric functions:
Solve a trigonometric equation:
Numerically find a root of a transcendental equation:
Plot the function to check if the solution is correct:
The zeros of CscDegrees:
The poles of CscDegrees:
Calculate residue symbolically and numerically:
FunctionExpand applied to CscDegrees generates expressions in trigonometric functions in radians:
ExpToTrig applied to the outputs of TrigToExp will generate trigonometric functions in radians:
CscDegrees is a numeric function:
Possible Issues (1)
Neat Examples (5)
Trigonometric functions are ratios that relate the angle measures of a right triangle to the length of its sides:
Solve trigonometric equations:
Add some condition on the solution:
Some arguments can be expressed as a finite sequence of nested radicals:
Plot CscDegrees at integer points:
Text
Wolfram Research (2024), CscDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/CscDegrees.html.
CMS
Wolfram Language. 2024. "CscDegrees." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CscDegrees.html.
APA
Wolfram Language. (2024). CscDegrees. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CscDegrees.html