How to use Cubic Hermite and Cubic Spline to interpolate Sine(x) with 4-5 non uniform samples?

Question

Task is to draw a curve of Sin(x) and then use Cubic Hermite and Cubic Spline to interpolate the sine wave with 4-5 non-uniform samples.

I've written a code to draw a sine wave but now I'm stuck how to implement the cubic (Hermite and Spline interpolation).

#include <conio.h>
#include <graphics.h>
#include <math.h>

int main(){

initwindow(800,600);
int x,y;
line(0,300,getmaxx(),300);
line(400,0,400,getmaxy());
float pi = 3.14;

for(int i = -360; i < 360 ; i++){

x = (int) 400+i;
y = (int) 300 - sin(i*pi/100)*25;
putpixel(x,y,WHITE);

}

getch();
closegraph();

return 0;

}

Expected result is to calculate Cubic Hermite and Cubic Spline interpolation on the sine(x) wave.