vectors.js

function Point(x, y) {
    this.x = x;
    this.y = y;
}

function Vector(degrees, length) {
    this.degrees = degrees; // -180 to 180
    this.length = length;
    this.radians = degrees * Math.PI / 180;
    
    // assuming y is up
    this.x = Math.cos(this.radians) * this.length;
    this.y = Math.sin(this.radians) * this.length;
}

function transform(point, vector) {
    return new Point(
        point.x + vector.x,
        point.y + vector.y
    );
}

var original = new Point(20, 200),
    offset = new Vector(60, 1000),
    transformed = transform(original, offset);
    
console.log(transformed.x); // 520.0000000000001
console.log(transformed.y); // 1066.0254037844386