Because I'm lazy, I hate programming, and it's not quite trivial given that "a" can be tan(b), parenthetical expressions, etc.
Shining light down on a plasma, and seeing where the ray intersects its surface. I can't solve it analytically since the plasma's surface has a funky transcendental shape, so I'm using Newton's method to find the solutions. For my initial guesses I quadratically expanded around a certain parameter of the plasma (something that I had absolutely no right to assume as being << 1), to get a cubic equation in the sine of the parametric variable for the plasma's surface. And that expression above is one of the solutions to that equation.
Thanks Mercator.
WTF is that thing anyway?
Shining light down on a plasma, and seeing where the ray intersects its surface. I can't solve it analytically since the plasma's surface has a funky transcendental shape, so I'm using Newton's method to find the solutions. For my initial guesses I quadratically expanded around a certain parameter of the plasma (something that I had absolutely no right to assume as being << 1), to get a cubic equation in the sine of the parametric variable for the plasma's surface. And that expression above is one of the solutions to that equation.
Thanks Mercator.
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