Error in Algebraic Construction or Computational Translation?

WhiskeyHammer

I have an equation that I've been trying to solve. I manipulated it until I had a=f(d) and then did by best to put it into a format the computer recognizes. However when I went back to check the results against the unsimplified version of the equation, they didn't work out as they should have; which tells me I screwed up manipulating the equation to a=f(d) or when I translated it from paper to program*. Im stumped.

If someone could take a look at my work for errors Id appreciate the second set of eyes.

Algebraic Manipulation:

Im fairly certain of my work until the fourth line, but if you need to see how I got there let me know.

Computational Form:
a=((-2)(x^5)(G)(q))/(((8)((D-x)^3)(n))-((G)(x^4)(q)(((tan(12))(pi)(D-x))+x)))
This is where I feel like the problem might be. Im relatively inexperienced using long equations in a computer setting.

*the third possibility being that I messed up checking the equation, but it seemed more prudent to start here

Integral

I can't see any problems with your algebra.

In your computation it looks like you have degrees in your trig function. Make sure your program is using degrees and not radians, or try converting to radians for the computation.

haruspex

Early on, there's a part of the right of the form P-d. By the end it has become P+d. Look at the step between the second and third lines from the end.

WhiskeyHammer

Yup, that was it. I failed to reverse distribute properly.

That should fix all the math that comes after this equation, but it'll take me a couple of days to work my way back through it all again. Its always the fast simple math that messes me up over a long process.

Thanks guys!

haruspex

Obvious, perhaps, but the way I track these things down is to plug in some values at the start and end of the manipulation and see if they agree. When I find a mismatch, I binary chop through the sequence of equations to find out where the value changed.