There are two ways you can check.
If you use a form:
First, consider that for a set of radio buttons (one doesn't make sense), they all are given the same name= , but can have different id= . They also, should each have a value= . When a button is checked, the data sent to the form (for that name'd group of radio buttons is that of the check item.
Locally, you may use the DOM and the id (which should be unique for every element on you page that has an id !). These have a checked property. You can test this value and determine which is checked.
Here's the DOM check for local usage:
var isChecked = document.getElementById(id).checked;