Implementation of sine function in C not working

I have attempted to implement the sine function in C, yet I am getting weird results. Here are the three functions I am using to calculate sine:

#define PI 3.14159265358979323846
#define DEPTH 16

double sine(long double);
long double pow(long double, unsigned int);
unsigned int fact(unsigned int);

double sine(long double x) {
    long double i_x = x *= PI/180;
    int n = 3, d = 0, sign = -1;

    // fails past 67 degrees
    for (; d < DEPTH; n += 2, d++, sign *= -1) {
        x += pow(i_x, n) / fact(n) * sign;
    }

    return x;
}

long double pow(long double base, unsigned int exp) {
    double answer = 1;
    while (exp) {
        answer *= base;
        exp--;
    }
    return answer;
}

unsigned int fact(unsigned int n) {
    unsigned int answer = 1;
    while (n > 1) {
        answer *= n--;
    }
    return answer;
}

To test it I have been testing it against the built in sine function as follows:

#include <stdlib.h>
#include <stdio.h>
#include <math.h>

main() {
    for (int i = 0; i <= 180; i++) {
        printf("sin(%i) = %lf, %lf\n", i, sine(i), sin(i*3.14159265358979323846/180));
    }

    exit(EXIT_SUCCESS);
}

Up through 67 degrees, it calculates the same as the built in function. Though, as it increases past 67 it typically strays gets further and further from the actual value.

Here is an example output:

>> sin(100) = 0.987711, 0.984808
>> sin(101) = 0.986885, 0.981627
>> sin(102) = 0.987056, 0.978148
>> sin(103) = 0.988830, 0.974370
>> sin(104) = 0.993060, 0.970296
>> sin(105) = 1.000948, 0.965926
>> sin(106) = 1.014169, 0.961262
>> sin(107) = 1.035052, 0.956305
>> sin(108) = 1.066807, 0.951057
>> sin(109) = 1.113846, 0.945519
>> sin(110) = 1.182194, 0.939693
>> sin(111) = 1.280047, 0.933580
>> sin(112) = 1.418502, 0.927184
>> sin(113) = 1.612527, 0.920505
>> sin(114) = 1.882224, 0.913545
>> sin(115) = 2.254492, 0.906308
>> sin(116) = 2.765192, 0.898794
>> sin(117) = 3.461969, 0.891007
              ...
>> sin(180) = 8431648.192239, 0.000000

Does anybody know why this is happening? I am using Visual Studio 2017 on Windows 7, if that provides any useful information.