Why don't Sin and Cos give expected results when rotating off axis around a non uniform shape?

Question

When I rotate a rectangle and draw straight lines along it's edge using Sin and Cos the lines don't follow the edge as the angle approaches 45 degrees, why? The exact same code works just fine when I use it on a square. See Gif:

Left object has the same width and height, No distortion of angles. Right side has larger X axis and lots of distortion.

Why does this happen and how do I prevent it?

Unity code:

[RequireComponent(typeof(Image))]
class rotation : MonoBehaviour
{
    [SerializeField]
    private float left = 180f, up = 90f;

    private void OnDrawGizmosSelected()
    {
        RectTransform rect = GetComponent<RectTransform>();

        Vector3[] corners = new Vector3[4];
        rect.GetWorldCorners(corners);
        float rot = transform.eulerAngles.z;

        Gizmos.color = Color.red;
        Gizmos.DrawLine(corners[3], corners[3] + new Vector3(
                Mathf.Cos((left + rot) * Mathf.Deg2Rad) * rect.rect.width,
                Mathf.Sin((left + rot) * Mathf.Deg2Rad) * rect.rect.height));

        Gizmos.color = Color.blue;
        Gizmos.DrawLine(corners[3], corners[3] + new Vector3(
            Mathf.Cos((up + rot) * Mathf.Deg2Rad) * rect.rect.width,
            Mathf.Sin((up + rot) * Mathf.Deg2Rad) * rect.rect.height));
    }
}

Answer 1

The length of the lines must always equal the length of the side. If you however multiply sin(angle) by the width of the rect and cos(angle) by the height, then if the angle point upwards, then the length of the line will be equal to the width of the rectangle and if the angle points sideways, then the length of the line will be equal to the height of the rectangle.

Do this instead:

Gizmos.DrawLine(corners[3], corners[3] + new Vector3(
    Mathf.Cos((left + rot) * Mathf.Deg2Rad) * rect.rect.width,
    Mathf.Sin((left + rot) * Mathf.Deg2Rad) * rect.rect.width)); // Change is here

Gizmos.color = Color.blue;
Gizmos.DrawLine(corners[3], corners[3] + new Vector3(
      Mathf.Cos((up + rot) * Mathf.Deg2Rad) * rect.rect.height, // Change is here
      Mathf.Sin((up + rot) * Mathf.Deg2Rad) * rect.rect.height));