Pretty printing degrees input to radians

I'm mostly concerned about edge cases, although I think I dealt with them all. Improvements on code quality would also be much appreciated.

/*
*/

if(degrees % 180 == 0) {
if(degrees == 180) {
return "π";
}
else if(degrees == -180){
return "-π";
}else{
return degrees / 180 + "π";
}
}

var frac = degrees / 180;

// 10 ** number of decimal places
var multiplier = Math.pow(10, frac.toString().split(".")[1].length);
var numerator = frac * multiplier;
var denominator = multiplier;

//http://stackoverflow.com/a/17445304/896112 - Euclid's Algorithm
function gcd(a, b) {
return (!b)?a:gcd(b, a%b);
}

var g = gcd(numerator, denominator);

numerator = numerator/g;
denominator = denominator/g;

if(numerator == 1){
numerator = "π";
}else if(numerator == -1){
numerator = "-π";
}else{
numerator += "π"
}

if(denominator < 0){
denominator = Math.abs(denominator);
numerator = "-"+numerator;
}

return numerator +"/"+ denominator;
}

-
printRadian(270) -> 2π/2 -> π is wrong, it should be 3π/2 – Caridorc Jan 9 at 18:27
Ok you fixed it in the comments, but does the code give the correct result for it? – Caridorc Jan 9 at 18:28
@Caridorc ah that was a typo, I added the comments after posting. Goes to show how good my math skills are :) – Carpetfizz Jan 9 at 18:29

Your code looks more complicated than necessary and some of your special cases are really not needed.

I will use an incremental development to avoid unnecessary code:

The first version is just based on the formula, with no additional prettiness:

function printRadians(angle) {
return angle + "π" + "/" + 180;
}

document.write([45, 90, 180, 270, 360, -45, -18].map(printRadians).join('  '));

Then we want to simplify the fraction, using, as you did, the gcd function:

function gcd(a, b) {
return (b == 0)?a:gcd(b, a%b);
}

var _gcd = gcd(angle, 180)
return angle / _gcd + "π" + "/" + 180 / _gcd;
}

document.write([45, 90, 180, 270, 360, -45, -18].map(printRadians).join('  '));

We are getting nearer, now we should take care of removing unnecessary ones:

function gcd(a, b) {
return (b == 0)?a:gcd(b, a%b);
}

var _gcd = gcd(angle, 180)
var numerator = angle / _gcd == 1 ? "" : angle / _gcd;
var denominator = 180 / _gcd == 1 ? "" : "/" + (180 / _gcd);
return numerator + "π" + denominator;
}

document.write([45, 90, 180, 270, 360, -45, -18].map(printRadians).join('  '));

And now let's put the minus in front of the numerator, not denominator:

function gcd(a, b) {
return (b == 0)?a:gcd(b, a%b);
}

document.write([45, 90, 180, 270, 360, -45, -18].map(printRadians).join('  '));
And we are done, just $4$ lines, with no lengthy ifs for special cases.