What is the curve? A circle or a parabola or something else?

Are you launching a rocket or a car?

Are you shooting a bullet or a canon ball? How fast is it going at the start?

And did you really mean 0.15 degrees? That is such a small angle that it is difficult to measure it by hand.

The slope is slightly positive to the left at -1. It is slightly negative to the right at +1.

A change of 0.15 degrees could mean that it starts at +0.075 degrees and changes to -0.075 degrees. Is this what you want?

You can readily approximate by assuming you have two back to back triangles and work it out that way.

For a mile long railroad track with 1 foot inserted, x is about 44 feet

Given the curve is a circle. First the circle must cut the abscissa at -1 and +1 which means it is symmetric in x so that the equation is x² + (y+a)² = r² where r is the radius and a the y offset to the center. Since the center is below the x axis a must be negative. We immediately obtain the result (y+a)²=r²-1. Similarly we obtain dy/dx = -x/sqrt(r²-1) (by substituting (y+a) after differentiation. This must still be less than tan(pi/1200) but we still have TWO unknowns r and a.

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then the radius of the circle is R = 1/sin(x) = 763.9439

and the height at the center is R(1 - cos(x)) = 0.0006545