Math Object Challenge: Update #2.

I have made substantial progress; using Taylor series, I approximated the sin, cos, sec, and csc functions. I also added summation and product and a few others. I now, however, have to lean on the use of ln and exp functions from the math object. I added a new function 'truncIf' that truncates a number if and only if the other parameter is an integer (that is, equal it itself when truncated). It is used to give more accurate results when using the pow command.

Code:

var atan = Math.atan;
var tan = Math.tan;
var pi = Math.PI;
var ln = Math.log;
var exp = Math.exp;

function ceil(x){
return (sgn(x))*(abs(x)+.5+div(atan(-tan(pi*(abs(x)+.5))),pi))+(x<0?1:0);
}

function floor(x){
return -ceil(-x);
}

function abs(x){
return sgn(x)*x;
}

function sgn(x){
return (x<0)?-1:(x>0)?1:0;
}

function div(x,y){
return x/y;
}

function sin(y){
var sign = sgn(y);
var x = abs(y);
while(x>2*pi){
x-=2*pi;
}
return (x - (pow(x,3)/fac(3)) + (pow(x,5)/fac(5)) - (pow(x,7)/fac(7)) + (pow(x,9)/fac(9)) - (pow(x,11)/fac(11)) + (pow(x,13)/fac(13)) - (pow(x,15)/fac(15)) + (pow(x,17)/fac(17)))*sign;
}

function cos(y){
var sign = sgn(y);
var x = abs(y);
while(x>2*pi){
x-=2*pi;
}
return (1 - (pow(x,2)/fac(2)) + (pow(x,4)/fac(4)) - (pow(x,6)/fac(6)) + (pow(x,8)/fac(8)) - (pow(x,10)/fac(10)) + (pow(x,12)/fac(12)) - (pow(x,14)/fac(14)) + (pow(x,16)/fac(16)))*sign;
}

function sec(x){
return 1/cos(x);
}

function csc(x){
return 1/sin(x);
}

function fac(x){
return product(1,x,"#");
}

function product(start,end,transform,inst){
var inst = inst || "#";
var out = 1;
transform = transform.split("");
for(i=0;i<transform.length;i++){
transform[i] = transform[i].replace(inst,"i");
}
transform = transform.join("");
for(i=start;i<=end;i++){
out*=eval(transform);
}
return out;
}

function sum(start,end,transform,inst){
var inst = inst || "#";
var out = 1;
transform = transform.split("");
for(i=0;i<transform.length;i++){
transform[i] = transform[i].replace(inst,"i");
}
transform = transform.join("");
for(i=start;i<=end;i++){
out+=eval(transform);
}
return out;
}

function pow(x,y){
return truncIf(x+y,exp(y*ln(x)));
}

function trunc(x){
return +(x+"").split(".")[0];
}

function truncIf(x,y){
return (trunc(x)==x)?trunc(y):y;
}