// 1-15-CSharp.cs

using System;

// C# has syntax similar to C++ and Java, but functions
// are members of classes. Here, MySin is a static method
// of the Trig class.

class MainClass {
    public static void Main() {
        double x = 3.2;

        Console.WriteLine($"Trig.MySin(x): {Trig.MySin(x)}");
        Console.WriteLine($"Math.Sin(x):   {Math.Sin(x)}");
        Console.WriteLine($"reference:     {-0.058374143427579909137}");

        Console.WriteLine(
            $"Trig.MySin(double.PositiveInfinity): " +
            $"{Trig.MySin(double.PositiveInfinity)}"
        );
    }
}

class Trig {
    // MySin(double x)
    //
    // Approximate sin(x) using the Taylor series
    //
    //                 x^3   x^5   x^7
    //     sin(x) = x - --- + --- - --- + ...
    //                  3!    5!    7!
    //
    // Rather than calculating each power and factorial
    // separately, calculate each term from the previous
    // term:
    //
    //                    x^2
    //     next = -term -----------,
    //                  n(n + 1)
    //
    // where n takes the values 2, 4, 6, ...
    public static double MySin(double x) {
        if (!double.IsFinite(x)) {
            return double.NaN;
        }

        double result = x;
        double term = x;

        for (double n = 2.0; ; n += 2.0) {
            term *= -(x/n)*(x/(n + 1.0));

            if (Math.Abs(term) < 1e-16) {
                break;
            }

            result += term;
        }

        return result;
    }
}