cos

Cosine of argument in radians

Syntax

Y = cos(X)

Description

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.

Examples

Plot Cosine Function

Plot the cosine function over the domain $$-\pi \le x\le \pi$$.

x = -pi:0.01:pi; 
plot(x,cos(x))
grid on

Cosine of Vector of Complex Angles

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

X — Input angle in radians

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

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

Y — Cosine of input angle

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

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

More About

Cosine Function

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

$$\text{cos}(\alpha )=\frac{\text{adjacent side}}{\text{hypotenuse}}=\frac{b}{h}.$$

The cosine of a complex argument, α, is

$$\text{cos}(\alpha )=\frac{e^{i\alpha }+e^{-i\alpha }}{2}.$$

Tips

• 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

Tall Arrays

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

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

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

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU 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 cos function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (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 cos 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.