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# Machining trygonometry

## Radius from 2 points on a curve ## Find the depth of a sphere section given the radius of the Sphere (R) and the radius of of the section (a)

If we have a spherical dish - and lay a straight line across the diameter - the depth (h) can be found.

Where R is the Radius of the sphere,
and a is the radius of the section(dish),
we find d - the depth of the section.  ## Depth of counter sinks \begin{align*}
A^2 + B^2 = C^2\\
y^2+B^2=r^2\\
r=B+x\\
y^2+B^2=(B+x)^2\\
y^2+B^2=B^2+2Bx+x^2\\
y^2-x^2=2Bx+x^2\\
B=\frac{y^2-x^2}{2x}\\
r=\frac{y^2-x^2}{2x}+x\\
r=\frac{y^2-x^2+2x^2}{2x}\\
r=\frac{y^2+x^2}{2x}\\
\end{align*}

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