Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











Sec






Mathematica Notation

Traditional Notation









Elementary Functions > Sec[z] > Introduction to the Secant Function in Mathematica





Automatic evaluations and transformations


For the exact argument , Mathematica returns an exact result.

For a machine‐number argument (numerical argument with a decimal point), a machine number is also returned.

The next inputs calculate 100‐digit approximations at and .

Within a second, it is possible to calculate thousands of digits for the secant function. The next input calculates 10000 digits for and analyzes the frequency of the digit in the resulting decimal number.

Here is a 50‐digit approximation to the secant function at the complex argument .

Mathematica automatically evaluates mathematical functions with machine precision, if the arguments of the function are numerical values and include machine‐number elements. In this case, only six digits after the decimal point are shown in the results. The remaining digits are suppressed, but can be displayed using the function InputForm.

Mathematica knows the symmetry and periodicity of the secant function. Here are some examples.

Mathematica automatically simplifies the composition of the direct and the inverse secant functions into its argument.

Mathematica also automatically simplifies the composition of the direct and any of the inverse trigonometric functions into algebraic functions of the argument.

In cases where the argument has the structure or , and or with integer , the secant function can be automatically transformed into trigonometric or hyperbolic secant or cosecant functions.

Sometimes simple arithmetic operations containing the secant function can automatically generate other equal trigonometric functions.

The secant function can be treated as a particular case of some more general special functions. For example, appears automatically from Bessel, Struve, Mathieu, Jacobi, hypergeometric, and Meijer functions for appropriate values of their parameters.