# sec

## Description

example

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

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Plot the secant over the domain $-\pi /2 and $\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

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

Data Types: single | double
Complex Number Support: Yes

## Output Arguments

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

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### Secant Function

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

The secant of a complex argument, α, is

$\text{sec}\left(\alpha \right)=\frac{2}{{e}^{i\alpha }+{e}^{-i\alpha }}\text{\hspace{0.17em}}.$

## 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.