sec

Secant of angle in radians

Syntax

Y = sec(X)

Description

Y = sec(X) returns the secant of the elements of X. The sec function operates element-wise on arrays. The function accepts both real and complex inputs.

For real values of X, sec(X) returns real values in the interval [-∞, -1] and [1, ∞].
For complex values of X, sec(X) returns complex values.

example

Examples

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Plot Secant Function

Open Live Script

Plot the secant over the domain $- π / 2 < x < π / 2$ and $π / 2 < x < 3 π / 2$ .

x1 = -pi/2+0.01:0.01:pi/2-0.01; 
x2 = pi/2+0.01:0.01:(3*pi/2)-0.01; 
plot(x1,sec(x1),x2,sec(x2)), grid on

Figure contains an axes object. The axes object contains 2 objects of type line.

Secant of Vector of Complex Angles

Open Live Script

Calculate the secant of the complex angles in vector x.

x = [-i pi+i*pi/2 -1+i*4];
y = sec(x)

y = 1×3 complex

   0.6481 + 0.0000i  -0.3985 + 0.0000i   0.0198 - 0.0308i

Input Arguments

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`X` — Input angle in radians
scalar | vector | matrix | multidimensional array | table | timetable

Input angle in radians, specified as a scalar, vector, matrix, multidimensional array, table, or timetable.

Data Types: single | double | table | timetable
Complex Number Support: Yes

Output Arguments

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`Y` — Secant of input angle
scalar | vector | matrix | multidimensional array | table | timetable

Secant of input angle, returned as real-valued or complex-valued scalar, vector, matrix, multidimensional array, table, or timetable.

More About

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Secant Function

The secant of an angle, α, defined with reference to a right angled triangle is

$sec (α) = \frac{1}{\cos (α)} = \frac{hypotenuse}{adjacent side} = \frac{h}{b} .$

Right triangle with vertices A, B, and C. The vertex A has an angle α, and the vertex C has a right angle. The hypotenuse, or side AB, is labeled as h. The opposite side of α, or side BC, is labeled as a. The adjacent side of α, or side AC, is labeled as b. The secant of α is defined as the hypotenuse h divided by the adjacent side b.

The secant of a complex argument, α, is

$sec (α) = \frac{2}{e^{i α} + e^{- i α}} .$

Tips

In floating-point arithmetic, sec is a bounded function. That is, sec does not return values of Inf or -Inf at points of divergence that are multiples of pi, but a large magnitude number instead. This stems from the inaccuracy of the floating-point representation of π.

Extended Capabilities

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Tall Arrays
Calculate with arrays that have more rows than fit in memory.

The sec function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment
Run code in the background using MATLAB® `backgroundPool` or accelerate code with Parallel Computing Toolbox™ `ThreadPool`.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The sec function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

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R2023a: Perform calculations directly on tables and timetables

The sec function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.

sec

Syntax

Description

Examples

Plot Secant Function

Secant of Vector of Complex Angles

Input Arguments

X — Input angle in radians scalar | vector | matrix | multidimensional array | table | timetable

Output Arguments

Y — Secant of input angle scalar | vector | matrix | multidimensional array | table | timetable

More About

Secant Function

Tips

Extended Capabilities

Tall Arrays Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

GPU Arrays Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Version History

R2023a: Perform calculations directly on tables and timetables

See Also

`X` — Input angle in radians
scalar | vector | matrix | multidimensional array | table | timetable

`Y` — Secant of input angle
scalar | vector | matrix | multidimensional array | table | timetable

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment
Run code in the background using MATLAB® `backgroundPool` or accelerate code with Parallel Computing Toolbox™ `ThreadPool`.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.