I would personally never say that “I believe that the sun rises in the East.” I would either say “the sun rises in the East” or “I think that sun rises in the East.” It’s not something that I need to believe. I can suspect that it does and then I can investigate further. In reality, the sun does not rise in the East anyway; it’s just an expression. The Earth rotates counter-clockwise about an axis that passes between the North and South poles in the direction towards the South Pole.
It’s possible to think something is one way or another, but at the same time to know that it’s based on a set of axioms and observations. Belief suggests that you think something is a certain way with a certainty that is not supported by evidence or a chain of reasoning based on reproducible observations.