3D Movement based off of facing direction

Question

I have a camera, with a yaw and pitch.

The position of the camera is x, y, and z.

I need a way to translate the yaw and a button press (WASD) to movement along the x and z.

So, I press W, and the camera matrix moves backwards, giving the appearance of moving forwards, based off of the yaw, but I don't know the formula to do so.

Camera class (I dont think its needed):

public static Vector3f position = new Vector3f(0, 1, 0);
public static double sensitivity;
private float pitch;
private float yaw;
private float roll;
private boolean escape;
private boolean fullscreen;

public Camera() {
    escape = false;
    fullscreen = false;
    Mouse.setGrabbed(true);
}

public void move() {
    if (Keyboard.isKeyDown(Keyboard.KEY_ESCAPE)) {
        if (escape == true) {
            Mouse.setGrabbed(true);
            Mouse.setCursorPosition(Display.getWidth()/2, 
            Display.getHeight()/2);
            escape = false;
        } else if (escape == false) {
            Mouse.setGrabbed(false);
            escape = true;
        }
    }
    //Not working rn
    if (Keyboard.isKeyDown(Keyboard.KEY_GRAVE) && escape == false) {
        if (fullscreen == true) {
            try {
                Display.setFullscreen(false);
            } catch (LWJGLException e) {
                e.printStackTrace();
            }
            fullscreen = false;
        } else {
            try {
                Display.setFullscreen(true);
            } catch (LWJGLException e) {
                e.printStackTrace();
            }
            fullscreen = true;
        }
    }
    //Change pitch based off of mouse y
    if (Mouse.getY() != Display.getHeight() / 2 && escape == false) {
        pitch += (Display.getHeight()/2 - Mouse.getY())/2;
        if (pitch > 360) {
            pitch = pitch % 360;
        }
    }
    //Change yaw with mouse movement
    if (Mouse.getX() != Display.getWidth() / 2 && escape == false) {
        yaw -= (Display.getWidth()/2 - Mouse.getX())/2;
        if (yaw > 360) {
            yaw = yaw % 360;
        }
    }
    //get out of the game
    if (escape == false) {
        Mouse.setCursorPosition(Display.getWidth() / 2, Display.getHeight() 
        /2);
    }

    //Here is the movement code, currently just moves along x/z normally
    if (Keyboard.isKeyDown(Keyboard.KEY_S) && escape == false) {
        position.x -= (Math.sin(yaw)*.2)*sensitivity;
    }

    if (Keyboard.isKeyDown(Keyboard.KEY_W) && escape == false) {
        position.x += (Math.sin(yaw)*.2)*sensitivity;
    }

    if (Keyboard.isKeyDown(Keyboard.KEY_A) && escape == false) {
        position.z -= (Math.cos(yaw)*.2)*sensitivity;
    }

    if (Keyboard.isKeyDown(Keyboard.KEY_D) && escape == false) {
        position.z += (Math.cos(yaw)*.2)*sensitivity;
    }

    if (Keyboard.isKeyDown(Keyboard.KEY_LSHIFT) && escape == false) {
        position.y -= 0.015;
    }

    if (Keyboard.isKeyDown(Keyboard.KEY_SPACE) && escape == false) {
        position.y += 0.015;
    }
}

public Vector3f getPosition() {
    return position;
}

public float getPitch() {
    return pitch;
}

public float getYaw() {
    return yaw;
}

public float getRoll() {
    return roll;
}

Thanks for reading.

EDIT:

Found a solution here [How to move my camera straight to mouse cursor, with any rotation?

For some reason if I look forwards my W moves forwards, if I look backwards I move backwards, but no in between

New code:

public static final Vector3f getRotationVector() { float r = (float) Math.toRadians(roll); Matrix4f mat = GameMath.createTransformationmatrix(new Vector3f(), pitch, yaw, 0, 1); Vector3f vector = new Vector3f(mat.m20, mat.m21, -mat.m22); return new Vector3f((float)(vector.x * Math.cos(r) + vector.y * Math.sin(r)), (float)(vector.y * Math.cos(r) - vector.x * Math.sin(r)), vector.z); }

Movement:

if (Keyboard.isKeyDown(Keyboard.KEY_S) && escape == false) {
        position.x -= getRotationVector().x;
        position.z -= getRotationVector().z;
    }

    if (Keyboard.isKeyDown(Keyboard.KEY_W) && escape == false) {
        position.x += getRotationVector().x;
        position.x += getRotationVector().z;
    }

    if (Keyboard.isKeyDown(Keyboard.KEY_A) && escape == false) {
        position.z -= getRotationVector().z;
        position.x -= getRotationVector().x;
    }

    if (Keyboard.isKeyDown(Keyboard.KEY_D) && escape == false) {
        position.z += getRotationVector().z;
        position.x += getRotationVector().x;
    }