How to rotate player camera via script?

I had my main camera as a component of my player object but I wanted to keep them separate so I created a script which allows for my camera to follow my player instead, while not keeping my camera as a child of the player object.

However, despite my player object itself being able to rotate properly, the camera does not follow it when I move my mouse horizontally, and only works vertically.

I currently have an empty game object with my main camera attached to it, with a reference to the player body (transform) and this following script:

public class FollowPlayer : MonoBehaviour
{

    public Transform player;
    public Vector3 offset;

    public float mouseSensitivity = 100f;

    float xRotation = 0f;

    void Start()
    {
        Cursor.lockState = CursorLockMode.Locked;
    }

    void Update()
    {
        // Make the camera follow the player
        transform.position = player.position + offset;

        float mouseX = Input.GetAxis("Mouse X") * mouseSensitivity * Time.fixedDeltaTime;
        float mouseY = Input.GetAxis("Mouse Y") * mouseSensitivity * Time.fixedDeltaTime;

        xRotation -= mouseY;
        xRotation = Mathf.Clamp(xRotation, -90f, 90f);

        transform.localRotation = Quaternion.Euler(xRotation, 0f, 0f);
        player.Rotate(Vector3.up * mouseX);

    }
}

If I put this camera back under my player object and take out the line with the 'offset', it works, but with the camera on its own, it doesn't.

I think I got it.

Instead of

transform.localRotation = Quaternion.Euler(xRotation, 0f, 0f);

Try doing

transform.rotation = Quaternion.Euler(xRotation, player.rotation.eulerAngles.y, 0f);

(edited)

So that the camera follows the Y rotation of the player as well, not just the position.

Hope this helps!

Alexa

Camera isn't rotating, because You rotate player object in script, not the camera-attached object. And You havn't any references in script on player horizontal rotation.
3DartBlade in first comment shows You how to make camera and player horizontal rotations equal [ transform.rotation = Quaternion.Euler(xRotation, player.rotation.euler.y, 0f); ] , but if You have offset from player, You wouldn't get desired behaviour of camera in such way.
Easyest way to achive desired behaviour (3D-person camera) is creating one more empty object with script:

public Transform player;
private void LateUpdate() {
    transform.position = player.transform.position;
    transform.rotation = player.transform.rotation;
}

And make Your empty object with attached camera child of previous object, with next script on it:

public Vector3 offset;
public float mouseSensitivity = 100f;
float xRotation = 0f;
void Start() {
    transform.position = cube.position + offset;
}
private void LateUpdate() {
    float mouseY = Input.GetAxis("Mouse Y") * mouseSensitivity * Time.deltaTime;
    xRotation -= mouseY;
    xRotation = Mathf.Clamp(xRotation, -90f, 90f);

    transform.localRotation = Quaternion.Euler(xRotation, 0f, 0f);
}

And, after that done, You should implement player rotation around Y-axis in PlayerController script. Controlling player in camera-controlling script make no sense. You can, of course, but it can make great problems in future.

And few notes:

1. You should move, or rotate Your Camera in LateUpdate() method, not in Update(). Because, otherwise it could lead to camera jittering.
2. NOT use Time.fixedDeltaTime in Update() or LateUpdate() methods. It make no sense and can lead to weard behaviours. Use it in FixedUpdate() method - when You work fith physics. In Update(), LateUpdate() use Time.deltaTime.
3. For advance and easy camera controll - using Cinemachine package is the best practice. You will loose some time to learn this tool (from 15 minutes to one hour), but it will make Your life much easyer in future.