calculate sin using math (functional series) | C++

#define _USE_MATH_DEFINES

#include <iostream>
#include <math.h>

double CalcFactorial(unsigned int n)
{
    if (n <= 1) return 1;

    double result = 1;

    for (size_t i = 1; i < n; i++)
    {
        result += result * i;
    }

    return result;
}

// - - - - - - - - - - - - - - - - - -

// Calc series sum from [start n] to [end n]
double CalcSeries(int startN, int endN, double (*func)(double))
{
    double result = 0.0;

    for (size_t n = startN; n <= endN; n++)
    {
        result += func(n);
    }

    return result;
}

// Calc functional series sum from [start n] to [end n]
double CalcSeries(int startN, int endN, double x, double (*func)(double, double))
{
    double result = 0.0;

    for (size_t n = startN; n <= endN; n++)
    {
        result += func(n, x);
    }

    return result;
}

// - - - - - - - - - - - - - - - - - -

double CalcSin(double x, int calcSteps)
{
    // Normalize argument to the range [-2pi, 2pi]
    {
        if (x > 2 * M_PI || x < 2 * M_PI)
        {
            x = fmod(x, 2 * M_PI);
        }
    }

    return CalcSeries(0, calcSteps, x,
        [] (double n, double x) {
            return pow(-1, n) * pow(x, 2 * n + 1) / CalcFactorial(2 * n + 1);
        }
    );
}

double CalcCos(double x, int calcSteps)
{
    return - CalcSin(x - M_PI_2, calcSteps);
}

// - - - - - - - - - - - - - - - - - -

void test(double t)
{
    int calcSteps = 10;

    printf_s("sin(%.2f):\n", t);
    printf_s("my_calc  = %8.5f\n", CalcSin(t, 10));
    printf_s("std_calc = %8.5f\n\n", sin(t));
}

// - - - - - - - - - - - - - - - - - -

int main()
{
    double input;

    while (true)
    {
        std::cin >> input;

        test(input);
    }

    return (0);
}

/*
Output:

-121
sin(-121.00):
my_calc  = -0.99882
std_calc = -0.99882

2
sin(2.00):
my_calc  =  0.90930
std_calc =  0.90930

6
sin(6.00):
my_calc  = -0.27939
std_calc = -0.27942

8
sin(8.00):
my_calc  =  0.98936
std_calc =  0.98936
*/