asec

Inverse secant in radians

Syntax

Y = asec(X)

Description

Y = asec(X) returns the Inverse Secant (sec^-1) of the elements of X in radians. The function accepts both real and complex inputs.

• For real values of X in the interval [-∞, -1] and [1, ∞], asec(X) returns values in the interval [0, π].

• For real values of X in the interval (-1, 1) and for complex values of X, asec(X) returns complex values.

Examples

Inverse Secant of a Value

Find the inverse secant of a value.

asec(-2.8)

ans = 
1.9360

Inverse Secant of a Vector of Complex Values

Find the inverse secant of the elements of vector x. The asec function acts on x element-wise.

x = [0.5i 1+3i -2.2+i];
Y = asec(x)

Y = 1×3 complex

   1.5708 + 1.4436i   1.4749 + 0.2970i   1.9503 + 0.1833i

Plot the Inverse Secant Function

Plot the inverse secant function over the intervals $$-5\le x\le -1$$ and $$1\le x\le 5$$.

x1 = -5:0.01:-1;
x2 = 1:0.01:5;
plot(x1,asec(x1),'b')
hold on
plot(x2,asec(x2),'b')
grid on

Input Arguments

X — Secant of angle

scalar | vector | matrix | multidimensional array | table | timetable

Secant of angle, specified as a scalar, vector, matrix, multidimensional array, table, or timetable. The asec operation is element-wise when X is nonscalar.

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

More About

Inverse Secant

The inverse secant is defined as

$${\sec }^{-1}(z)={\cos }^{-1}\left(\frac{1}{z}\right).$$

Extended Capabilities

Tall Arrays

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

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

C/C++ Code Generation
Generate C and C++ code using MATLAB® 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 asec function supports GPU array input with these usage notes and limitations:

• If the output of the function running on the GPU can be complex, then you must explicitly specify its input arguments as complex. For more information, see Work with Complex Numbers on a GPU (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 asec 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.