XNA Vector2 Rotation Question

Question

I'm messing about with some stuff in XNA and am trying to move an object around asteroids-style in that you press left and right to rotate and up/down to go forwards and backwards in the direction you are pointing.

I've got the rotation of the sprite done, but i can't get the object to move in the direction you've pointed it, it always moves up and down on the x = 0 axis.

I'm guessing this is straight forward but I just can't figure it out. My "ship" class has the following properties which are note worthy here:

Vector2 Position
float Rotation

The "ship" class has an update method is where the input is handled and so far I've got the following:

public void Update(GameTime gameTime)
{
    KeyboardState keyboard = Keyboard.GetState();
    GamePadState gamePad = GamePad.GetState(PlayerIndex.One);

    float x = Position.X;
    float y = Position.Y;

    if (keyboard.IsKeyDown(Keys.Left))  Rotation -= 0.1f;
    if (keyboard.IsKeyDown(Keys.Right)) Rotation += 0.1f;
    if (keyboard.IsKeyDown(Keys.Up))    ??;
    if (keyboard.IsKeyDown(Keys.Down))  ??;

    this.Position = new Vector2(x, y);
}

Any help would be most appreciated!

Answer 1

I believe the general formula is

X += cos(Angle * PI/180)*Speed
Y += sin(Angle * PI/180)*Speed

Here is an example:

 public partial class Form1 : Form
    {
        private float X = 10, Y=10;
        private float Angle = 45f;
        float PI = 3.141f;


        public Form1()
        {
            InitializeComponent();
        }

        private void button1_Click(object sender, EventArgs e)
        {           
            X += (float)Math.Cos(Angle * PI / 180.0f)*5f;
            Y += (float)Math.Sin(Angle * PI / 180.0f) * 5f;

            button1.Top = (int)X;
            button1.Left = (int)Y;
        }
    }

Answer 2

OK, so here's how I did it (I knew there would be a non-trig solution!)

float x = Position.X;
float y = Position.Y;

Matrix m = Matrix.CreateRotationZ(Rotation);

if (keyboard.IsKeyDown(Keys.Left))  Rotation -= 0.1f;
if (keyboard.IsKeyDown(Keys.Right)) Rotation += 0.1f;
if (keyboard.IsKeyDown(Keys.Up))
{
    x += m.M12 * 5.0f;
    y -= m.M11 * 5.0f;
}
if (keyboard.IsKeyDown(Keys.Down))
{
    x -= m.M12 * 5.0f;
    y += m.M11 * 5.0f;
}