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.

Examples

Plot Secant Function

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

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

Secant of Vector of Complex Angles

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

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

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

Secant Function

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

$$\text{sec}(\alpha )=\frac{1}{\cos \left(\alpha \right)}=\frac{\text{hypotenuse}}{\text{adjacent side}}=\frac{h}{b}.$$

The secant of a complex argument, α, is

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

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

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

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.