# How to find 4 unknowns?

There are 4 unknowns constants: a,b,c,p. The variable is phi and the result is d.

For phi={13,23,45,73} the results are d={32.08754292290807,32.1136624112758,32.1728430675844,32.2430287624866}

The equation is:

(c/0.3048*((1+(a*p/(b*c))*(sin(phi*pi/180))^2))/sqrt(1-sqrt(1-b^2/a^2)*
((sin(phi*pi/180))^2))) = d


How can I solve it in Mathematica?

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Have a look at Solve. – b.gatessucks Oct 31 '12 at 13:47

If I decipher your parentheses correctly, this is just a second order algebraic equation in u if you set u=Sin[phi]^2. So you may directly define a function

f[a_,b_,c_,p_] := Block[{A,B,C,Delta,U},
A=...;B=...;C=...;Delta=Sqrt[B^2-4*A C];
U=...;
phi=ArcSin[Sqrt[U]];]


which first solves the equation in u, then takes the arcsin.

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Note that C is protected! – sebhofer Oct 31 '12 at 16:11
@sebhofer It's inside a Block :) – R. M. Oct 31 '12 at 16:18
@rm-rf Damn ... – sebhofer Oct 31 '12 at 16:37
– Dr. belisarius Oct 31 '12 at 17:54
Thank you, I' m able to do second order algebraic equation but I don't known how to solve it. Can you provide exact code (or How can I put there all 4 solutions i.e. (For phi={13,23,45,73} the results are d=32.08754292290807,32.1136624112758,32.1728430675844,32.2430287624866})) Thank you in advance. Milos – Milos Oct 31 '12 at 18:20