I have the following equation:
eq = 0.003101895368576676` f - 500000/(1057 f \[Pi]) - (0.43169299511061626` Cos[0.019329990640367303` f] Sin[0.019329990640367303` f])/(1.0609` (1.37`*^-11 + 0.222185005727138`*^-7 Sqrt[f])^2 Cos[0.019329990640367303` f]^2 + Sin[0.019329990640367303` f]^2) == 0
Mathematica does not seem to be able to solve it for any of it's roots, f.
NSolve[eq, f]
Just returns the input. Same with Solve[]. However, I can plot the left hand side without any problems:
Plot[(eq // First) /. f -> freq, {freq, 20, 2000}]
So how come Mathematica can't find any numerical solutions?
NSolve
: NSolve deals primarily with linear and polynomial equations. So it's not surprising to find it fail on transcendental equation. You may want to read this: mathematica.stackexchange.com/q/91784/1871 $\endgroup$