finding the value of a in my fresnel equation

hi all, need helping find the value of a from the following equation:

1st i defined my fresnelc function:

>> syms a
>> F = a*int(cos((pi/2)*u^2),u,0,((0.01*a)/(pi)))
 
F =
 
a*fresnelc(a/(100*pi))

then i used F and the "solve command" to find the answer to a:

double( solve (atan((-1*((F)-62.811))/(sqrt((100^2)-((F)-62.811)^2)))-(0.000015915)*(a^2), a ) )
Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve. 
> In solve (line 304) 

ans =

 -115.0075

the answer should be = 200, but it gives me -115.2 , please do tell me if im doing anything wrong, just for reference im attaching the actual function as well:

please do let me know if im going wrong somewhere in the matlab command???

best regards,

Rehan

[David Hill]

double( solve (atan((-F+62.811)/sqrt(100^2-(F-62.811)^2)-(0.000015915)*(a^2), a ) ))

I cleaned up the equation some and I am getting +115.2853

[Rehanos_boyzee]

Thanks David,

I can see you removed alot of brackets and cleaned the solution, thanks. Good atleast its positive now, but still in the reference the value comes out to be equal to a=200. which is why i felt im doing something wrong. did notice any other mistakes in my working methods?

please do let me know,

regards,

Rehan

Answer 1

[Walter Roberson]

You are not going to get a closed form solution, so there is no point using solve() .

Instead you should use vpasolve(). vpasolve() permits you to pass in an initial guess, or even a search range, as the third parameter.

And remember you can

syms s
assume(s>0)