# cospi

Compute cos(X*pi) accurately

## Syntax

``Y = cospi(X)``

## Description

example

````Y = cospi(X)` computes `cos(X*pi)` without explicitly computing `X*pi`. This calculation is more accurate than `cos(X*pi)` because the floating-point value of `pi` is an approximation of π. In particular: For odd integers, `cospi(n/2)` is exactly zero.For integers, `cospi(n)` is +1 or -1. ```

## Examples

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Compare the accuracy of `cospi(X)` vs. `cos(X*pi)`.

Create a vector of values.

`X = [0 1/2 1 3/2 2];`

Calculate the cosine of `X*pi` using the normal `cos` function.

`Y = cos(X*pi)`
```Y = 1×5 1.0000 0.0000 -1.0000 -0.0000 1.0000 ```

The results contain small numerical errors due to the fact that `pi` is a floating-point approximation of the true value of $\pi$. For instance, `Y(2)` is not exactly zero even though $\mathrm{cos}\left(\frac{\pi }{2}\right)=0$.

`Y(2)`
```ans = 6.1232e-17 ```

Use `cospi` to calculate the same values. In this case, the results are exact.

`Z = cospi(X)`
```Z = 1×5 1 0 -1 0 1 ```
`Z(2)`
```ans = 0 ```

## Input Arguments

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

Data Types: `single` | `double`
Complex Number Support: Yes