How to make the player walk in the direction it is pointing?

Question

I made a simple movement system in Unity 3D, but I don't know how to make it so that I move in the direction my player is pointing in.

using UnityEngine;

public class PlayerControler : MonoBehaviour
{
    CharacterController characterController;
    public float MovementSpeed = 1f;
    public float Gravity = 9.8f;
    private float velocity = 0f;
    void Start()
    {
        characterController = GetComponent<CharacterController>();
    }
    void Update()
    {
        float horizontal = Input.GetAxis("Horizontal") * MovementSpeed;
        float vertical = Input.GetAxis("Vertical") * MovementSpeed;
        characterController.Move((Vector3.right * horizontal + Vector3.forward * vertical) * Time.deltaTime);
        if (characterController.isGrounded)
        {
            velocity = 0;
        }
        else
        {
            velocity -= Gravity * Time.deltaTime;
            characterController.Move(new Vector3(0, velocity, 0));
        }
    }
}

This is the player controller.

using UnityEngine;
public class MouseControl : MonoBehaviour
{
    public float horizontalSpeed = 1f;
    public float verticalSpeed = 1f;
    private float xRotation = 0.0f;
    private float yRotation = 0.0f;
    private Camera cam;
    void Start()
    {
        cam = Camera.main;
    }
    void Update()
    {
        float mouseX = Input.GetAxis("Mouse X") * horizontalSpeed;
        float mouseY = Input.GetAxis("Mouse Y") * verticalSpeed;
        yRotation += mouseX;
        xRotation -= mouseY;
        xRotation = Mathf.Clamp(xRotation, -90f, 90f);
        cam.transform.eulerAngles = new Vector3(xRotation, yRotation, 0.0f);
    }
}

This is the code that makes my character face where my cursor is.

Edit: This is a First-Person 3D game. The player has a CharacterControler component on it, and the Main Camera is a child of the player. The second piece of code changes the direction that the camera is facing when the cursor is moved. The first script is the movement script, and utilises the CharacterController component of the player to move. I want to make to that instead of going in four static directions every time I press a movement key, I want the player to move in proportion to the direction that the camera is facing (on the X axis). E.g: If I am facing West and I press “W” to go forwards, I want the character to go West instead of North.

Answer 1

@derHugo was right, but I forgot to update the angles in the player movement script, so it always thought that I was rotated 0,0,0.

using UnityEngine;
public class PlayerControler : MonoBehaviour
{
    Vector3 angles;
    CharacterController characterController;
    MouseControl mouseControl;
    public float MovementSpeed = 1f;
    public float Gravity = 9.8f;
    private float velocity = 0f;
    void Start()
    {
        characterController = GetComponent<CharacterController>();
        mouseControl = GetComponent<MouseControl>();
    }
    void Update()
    {
        angles = new Vector3(mouseControl.xRotation, mouseControl.yRotation, 0f);
        transform.eulerAngles = angles;
        float horizontal = Input.GetAxis("Horizontal") * MovementSpeed;
        float vertical = Input.GetAxis("Vertical") * MovementSpeed;
        characterController.Move((transform.right * horizontal + transform.forward * vertical) * Time.deltaTime);
        if (characterController.isGrounded)
        {
            velocity = 0;
        }
        else
        {
            velocity -= Gravity * Time.deltaTime;
            characterController.Move(new Vector3(0, velocity, 0));
        }
    }
}

Updated code Note: I had to made the X and Y rotation variables public.

[HideInInspector]public float xRotation = 0.0f;
[HideInInspector]public float yRotation = 0.0f;

Answer 2

Instead of the global vectors Vector3.forward and Vector3.right in

characterController.Move((Vector3.right * horizontal + Vector3.forward * vertical) * Time.deltaTime);

rather use your local direction vectors Transform.forward and Transform.right

characterController.Move((transform.right * horizontal + transform.forward * vertical) * Time.deltaTime);