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Hyperbolic cosine


Y = cosh(X)



Y = cosh(X) returns the hyperbolic cosine of the elements of X. The cosh function operates element-wise on arrays. The function accepts both real and complex inputs. All angles are in radians.


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Create a vector and calculate the hyperbolic cosine of each value.

X = [0 pi 2*pi 3*pi];
Y = cosh(X)
Y = 1×4
103 ×

    0.0010    0.0116    0.2677    6.1958

Plot the hyperbolic cosine function over the domain -5x5.

x = -5:0.01:5; 
y = cosh(x);
grid on

The hyperbolic cosine satisfies the identity cosh(x)=ex+e-x2. In other words, cosh(x) is the average of ex and e-x. Verify this by plotting the functions.

Create a vector of values between -3 and 3 with a step of 0.25. Calculate and plot the values of cosh(x), exp(x), and exp(-x). As expected, the curve for cosh(x) lies between the two exponential curves.

x = -3:0.25:3;
y1 = cosh(x);
y2 = exp(x);
y3 = exp(-x);
grid on

Input Arguments

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

Data Types: single | double
Complex Number Support: Yes

More About

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Hyperbolic Cosine

The hyperbolic cosine of an angle x can be expressed in terms of exponential functions as


In terms of the traditional cosine function with a complex argument, the identity is


Extended Capabilities

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

See Also

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Introduced before R2006a