Faith is belief without proof.
To interject a little. Often in Christian circles, faith is described at expecting things that have not yet happened (Heb 11:1). If we use this terminology, any belief that something will happen in the future would be classified as faith.
But... if you have proof then you don't need faith. Past personal observation, history, science, math, and orbital mechanics all say that the sun will come up tomorrow. Faith is not needed.
But, it may not. You don't have proof until it happens. I can show that it came up this morning. I cannot show that it is coming up tomorrow. What you are stuck with is a prediction from the hypothesis.