Math Trigonometric Functions in .NET

Overview

This C# library provides implementations of all standard trigonometric functions, including basic functions like sine, cosine, and tangent, as well as their hyperbolic counterparts, inverse functions, and more. This library is designed to offer a comprehensive set of tools for mathematical, engineering, and scientific applications requiring trigonometric calculations.

Missing Trigonometric Functions in .NET

The .NET includes basic trigonometric functions (sin, cos, tan, asin, acos, atan) and their hyperbolic counterparts (sinh, cosh, tanh, asinh, acosh, atanh) in the Math class. However, the following trigonometric functions are missing in .NET and are implemented in this library:

1. Cot (Cotangent)
2. Sec (Secant)
3. Csc (Cosecant)
4. Acot (Inverse Cotangent)
5. Asec (Inverse Secant)
6. Acsc (Inverse Cosecant)
7. Coth (Hyperbolic Cotangent)
8. Sech (Hyperbolic Secant)
9. Csch (Hyperbolic Cosecant)
10. Acoth (Inverse Hyperbolic Cotangent)
11. Asech (Inverse Hyperbolic Secant)
12. Acsch (Inverse Hyperbolic Cosecant)

You can find a detailed explanation of the implementation and approach in my article on Medium.

Installation

You can install this library via NuGet Package Manager. To do this, follow these steps:

1. Open your project in Visual Studio.

2. Go to Tools > NuGet Package Manager > Manage NuGet Packages for Solution.

3. Search for MathTrigonometric.

4. Select the package and click Install. Alternatively, you can install the package using the NuGet Package Manager Console:

    Install-Package MathTrigonometric
   

Functions Included

In version 1.1.0, support for complex numbers has been introduced through overloaded methods for the trigonometric functions listed below. This allows the library to handle both real and complex inputs seamlessly.

Basic Trigonometric Functions

1. Sin

   Sine of the angle is ratio of the opposite leg to hypotenuse.

   double Sin(double a);
   

   • Input: Angle in radians (any real number).
   • Output: The sine of the input angle in range: [-1, 1].

2. Cos

   Cosine of the angle is ratio of the adjacent leg to hypotenuse.

    double Cos(double a);
   

   • Input: Angle in radians (any real number).
   • Output: The cosine of the input angle in range: [-1, 1].

3. Tan

   Tangent of the angle is ratio of the opposite leg to adjacent one.

    double Tan(double a);
   

   • Input: Angle in radians (any real number).
   • Output: The tangent of the input angle (any real number).

4. Cot

   Cotangent of the angle is ratio of the adjacent leg to opposite one.

    double Cot(double a);
   

   • Input: Angle in radians (any real number).
   • Output: The cotangent of the input angle (any real number).

5. Sec

   Secant of the angle is ratio of the hypotenuse to adjacent leg.

    double Sec(double a);
   

   • Input: Angle in radians (any real number).
   • Output: The secant of the input angle in range: (-∞, -1] ∪ [1, ∞).

6. Csc

   Cosecant of the angle is ratio of the hypotenuse to opposite leg.

    double Csc(double a);
   

   • Input: Angle in radians (any real number).
   • Output: The cosecant of the input angle in range: (-∞, -1] ∪ [1, ∞).

Inverse Trigonometric Functions

7. Asin

   Arc sine is inverse of the Sine function.

    double Asin(double d);
   

   • Input: Value in range: [-1, 1].
   • Output: Angle in radians is limited to the range [−π/2, π/2].

8. Acos

   Arc cosine is inverse of the Cosine function.

    double Acos(double d);
   

   • Input: Value in range: [-1, 1].
   • Output: Angle in radians is limited to the range [0, π].

9. Atan

   Arc tangent is inverse of the Tangent function.

    double Atan(double d);
   

   • Input: Any real number.
   • Output: Angle in radians is limited to the range (−π/2, π/2).

10. Acot

    Arc cotangent is inverse of the Cotangent function.

    double Acot(double d);
    

    • Input: Any real number.
    • Output: Angle in radians is limited to the range (0, π).

11. Asec

    Arc secant is inverse of the Secant function.

    double Asec(double d);
    

    • Input: Value in range: (-∞, -1] ∪ [1, ∞).
    • Output: Angle in radians is limited to the range [0, π/2)∪(π/2, π].

12. Acsc

    Arc cosecant is inverse of the Cosecant function.

    double Acsc(double d);
    

    • Input: Value in range: (-∞, -1] ∪ [1, ∞).
    • Output: Angle in radians is limited to the range [−π/2, 0)∪(0, π/2].

Hyperbolic Trigonometric Functions

13. Sinh

    Hyperbolic sine is defined as Sinh(x) = (e^x − e^−x)/2.

    double Sinh(double x);
    

    • Input: Any real number.
    • Output: Value (any real number).

14. Cosh

    Hyperbolic cosine is defined as Cosh(x) = (e^x + e^−x)/2.

    double Cosh(double x);
    

    • Input: Any real number.
    • Output: Value in range: [1, +∞).

15. Tanh

    Hyperbolic tangent is defined as Tanh(x) = (e^x − e^−x)/(e^x + e^−x).

    double Tanh(double x);
    

    • Input: Any real number.
    • Output: Value in range: (-1, 1).

16. Coth

    Hyperbolic cotangent is defined as Coth(x) = (e^x + e^−x)/(e^x − e^−x).

    double Coth(double x);
    

    • Input: Value in range: (−∞, 0)∪(0, +∞).
    • Output: Value in range: (−∞, -1)∪(1, +∞).

17. Sech

    Hyperbolic secant is defined as Sech(x) = 2/(e^x + e^−x).

    double Sech(double x);
    

    • Input: Any real number.
    • Output: Value in range: (0, 1].

18. Csch

    Hyperbolic cosecant is defined as Csch(x) = 2/(e^x − e^−x).

    double Csch(double x);
    

    • Input: Value in range: (−∞, 0)∪(0, +∞).
    • Output: Value in range: (−∞, 0)∪(0, +∞).

Inverse Hyperbolic Trigonometric Functions

19. Asinh

    Arc-hyperbolic sine is inverse of the Hyperbolic sine function is defined as Arsinh(x) = ln[x + √(x^2 + 1)].

    double Asinh(double x);
    

    • Input: Any real number.
    • Output: Value (any real number).

20. Acosh

    Arc-hyperbolic cosine is inverse of the Hyperbolic cosine function is defined as Arcosh(x) = ln[x + √(x^2 - 1)].

    double Acosh(double x);
    

    • Input: Value in range: [1, +∞).
    • Output: Value in range: [0, +∞).

21. Atanh

    Arc-hyperbolic tangent is inverse of the Hyperbolic tangent function is defined as Artanh(x) = ln[(1 + x)/(1 − x)]/2.

    double Atanh(double x);
    

    • Input: Value in range: (-1, 1).
    • Output: Value (any real number).

22. Acoth

    Arc-hyperbolic cotangent is inverse of the Hyperbolic cotangent function is defined as Arcoth(x) = ln[(1 + x)/(x − 1)]/2.

    double Acoth(double x);
    

    • Input: Value in range: (−∞, -1)∪(1, +∞).
    • Output: Value in range: (−∞, 0)∪(0, +∞).

23. Asech

    Arc-hyperbolic secant is inverse of the Hyperbolic secant function is defined as Arsech(x) = ln([1 + √(1 − x^2)]/x).

    double Asech(double x);
    

    • Input: Value in range: (0, 1].
    • Output: Value in range: [0, +∞).

24. Acsch

    Arc-hyperbolic cosecant is inverse of the Hyperbolic cosecant function is defined as Arcsch(x) = ln[1/x + √(1/(x^2) + 1)].

    double Acsch(double x);
    

    • Input: Value in range: (−∞, 0)∪(0, +∞).
    • Output: Value in range: (−∞, -0)∪(0, +∞).

Extra functions

25. DegreesToRadians

    Converts degrees to radians.

    double DegreesToRadians(double degrees);
    

    • Input: Angle in degrees (any real number).
    • Output: Angle in radians (any real number).

26. RadiansToDegrees

    Converts radians to degrees.

    double RadiansToDegrees(double radians);
    

    • Input: Angle in radians (any real number).
    • Output: Angle in degrees (any real number).

How to use trigonometry in C#

Here are some examples of how to use the trigonometric functions in this library:

Basic Trigonometric Functions

using MathTrigonometric;

class Program
{
    static void Main()
    {
        double angle = Math.PI / 4; // 45 degrees in radians

        double sine = MathTrig.Sin(angle);
        double cosine = MathTrig.Cos(angle);
        double tangent = MathTrig.Tan(angle);
        double cotangent = MathTrig.Cot(angle);
        double secant = MathTrig.Sec(angle);
        double cosecant = MathTrig.Csc(angle);

        Console.WriteLine($"Sin({angle}) = {sine}");
        Console.WriteLine($"Cos({angle}) = {cosine}");
        Console.WriteLine($"Tan({angle}) = {tangent}");
        Console.WriteLine($"Cot({angle}) = {cotangent}");
        Console.WriteLine($"Sec({angle}) = {secant}");
        Console.WriteLine($"Csc({angle}) = {cosecant}");
    }
}

Inverse Trigonometric Functions

using MathTrigonometric;

class Program
{
    static void Main()
    {
        double value = 0.5;

        double angleAsin = MathTrig.Asin(value);
        double angleAc