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Cosine of argument in radians


Y = cos(X) returns the cosine for each element of X. The cos function operates element-wise on arrays. The function accepts both real and complex inputs.

  • For real values of X, cos(X) returns real values in the interval [-1, 1].

  • For complex values of X, cos(X) returns complex values.


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Plot the cosine function over the domain -πxπ.

x = -pi:0.01:pi; 
grid on

Calculate the cosine of the complex angles in vector x.

x = [-i pi+i*pi/2 -1+i*4];
y = cos(x)
y = 1×3 complex

   1.5431 + 0.0000i  -2.5092 - 0.0000i  14.7547 +22.9637i

Input Arguments

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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

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Cosine of input angle, returned as a real-valued or complex-valued scalar, vector, matrix, multidimensional array, table, or timetable.

More About

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Cosine Function

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

cos(α)=adjacent sidehypotenuse=bh.

Right triangle with vertices A, B, and C. The vertex A has an angle α, and the vertex C has a right angle. The hypotenuse, or side AB, is labeled as h. The opposite side of α, or side BC, is labeled as a. The adjacent side of α, or side AC, is labeled as b. The cosine of α is defined as the adjacent side b divided by the hypotenuse h.

The cosine of a complex argument, α, is



  • To compute cos(X*pi) accurately, without using pi as a floating-point approximation of π, you can use the cospi function instead. For example, cospi(m/2) is exactly zero for odd integers m and cospi(n) is +1 or –1 for integers n.

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™.

Version History

Introduced before R2006a

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See Also

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