How can I convert quaternion to radians without being a math major?

Question

I am making a small game as a side project and part of the game includes a ball being launched from a cannon. I need to be able to track the and of the rotating cannon to know where to instantiate the ball. I understand the trig behind tracking a point on the circumference of a circle but I just don't know how to convert the quaternion values I get from the transform.rotation to radians/degrees so I can use them in trig functions.

Just using the quaternion values in my trig functions didn't work, as you may expect. I am very new to C# so I'm sure there is a much more elegant solution to this and I am probably doing more work than necessary but this is still something I'd like to know regardless. I appreciate any insight you guys may have on this and can you please talk to me like a 5-year-old because I'm having a hard time conceptualizing quaternions.

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class Launcher : MonoBehaviour
{

    public GameObject ball;
    public float posX;
    public float posY;
    public float radians;

    // Start is called before the first frame update
    void Start()
    {
    
    }

    // Update is called once per frame
    void Update()
    {

        //convert the degrees to radians
        radians = (float)((transform.rotation.z) * (System.Math.PI / 180));

        posX = (float) System.Math.Cos(radians);
        posY = (float) System.Math.Sin(radians);

        if(Input.GetKeyDown(KeyCode.S)) {
            Instantiate(ball, new Vector3(posX, posY + transform.position.y, transform.position.z), transform.rotation);
        }
    }
}

Answer 1

You don't have to convert the quaternion into another representation to do this. The Transform class from Unity provides a way to rotate and translate a vector given a transform. Assuming that the tip of the cannon in local coordinates is (1,0,0), you can calculate the position of the ball like this:

var localBallPosition = new Vector3(1,0,0);
var worldBallPosition = transform.TransformPoint(localBallPosition);

localBallPosition should be made to fit the length of the cannon.