Computing the cosine of an angle is a fundamental operation in fields like mathematics, physics, and computer science. In this article, we will construct a program in Haskell–a powerful functional programming language–to perform this operation accurately and efficiently.

Haskell equips us with mathematical functions and libraries that allow us to perform these tasks quite smoothly. Let’s dive into the step-by-step process and see how it unfolds.

import Data.Number.Fixed (cos, E10) computeCos :: Double -> Double computeCos x = cos (pi / 180 * x)

In the Haskell code snippet above, we employ the ‘cos’ function from the Data.Number.Fixed library to compute the cosine value. The ‘pi / 180 * x’ expression is used to convert the angle from degrees to radians since the ‘cos’ function expects its argument in radians.

**The ‘computeCos’ function is a representation of one of the powerful ways in which Haskell, a purely functional programming language, can be utilized to perform mathematical computations.**

## The Data.Number.Fixed Library in Haskell

The Data.Number.Fixed library in **Haskell provides several functions related to fixed-precision arithmetic**. It allows the type checks during compile-time for precision, which ensures wide support for mathematical operations.

In this library, functions like sin, cos, tan, asin, acos, atan, sinh, cosh, tanh and many more are available for use. These functions relieve us of the burden of writing out complex mathematical functions manually, making code more readable and maintainable.

## The Role of The Cos Function

In Haskell, **mathematical functions, especially trigonometric ones, are an essential part of numerous scientific computations**. The `cos` function, in particular, has wide ranging use cases – from rendering 3D graphics, to solving mathematical equations, and even simulating physical phenomena. These functions in Haskell provide an accurate and efficient method for performing such calculations.

Equally important is the process of converting degrees to radians, allowing for the proper usage of these functions. This can be performed using the expression ‘pi / 180 * x’, as seen in the ‘computeCos’ function we’ve defined.

**To summarize, once we’re equipped with the right libraries and tools, writing a program to compute the cosine of an angle in Haskell is a clean and straightforward task. ** Haskell’s mathematical libraries represent one of the many powerful features offered by this pure, functional programming language.