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Secant of angle in radians



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.


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Plot the secant over the domain -π/2<x<π/2 and π/2<x<3π/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. The axes contains 2 objects of type line.

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.

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)=1cos(α)=hypotenuseadjacent side=hb.

The secant of a complex argument, α, is



  • 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

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

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

See Also

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Introduced before R2006a