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.

This 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™.

This function fully supports GPU arrays. 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.