Is a 1 degree rotation of a point possible?

[Cyclopse]

Let's say the center of a circle on a graph is (0,0), and the point at the circumference is (-7,24).

Do you think it is possible to find a point that is not on the lattice point using a 1 degree rotation?

^By that I mean if it is possible to do a 1 degree rotation of the point to find a nonlattice point.

 

[HallsofIvy]

I'm afraid I don't understand your question. You have a circle with center at (0, 0) and (-7, 24) is on the circumference (so the equation of the circle is [itex]x^2+ y^2= 625[/itex]). You then ask "is it possible to find a point that is not on the lattice point using a 1 degree rotation?"

What lattice point? What lattice? Do you mean the lattice of points (x, y) where x and y are both integer? Or the lattice of points (x,y) where x and y are both rational? Or some other lattice?
Are you asking "Does there exist an integer n such that both [itex]25 cos(n)[/itex] and [itex]25 sin(n)[/itex] are integer (or rational)?