"Cannot find explicit solution"

The Matlab says "Cannot find explicit solution". Please help.

syms t1;
x=15*10^(-6)*sin(2.76*10^7*(1.5*10^(-7)+t1));
phi=x/(200*10^(-6));
c=abs(414*t1*cos(pi/4)-18*10^(-6));
d=200*10^(-6)-414*t1*sin(pi/4);
beta=c/d;
f=phi-beta==0;
solve(f,t1);
disp(t1)
----------------------------
Warning: Cannot find explicit solution. 
> In solve (line 318)
In Untitled2 (line 8) 
t1

Also, maybe there will be many solutions about t1. I need the minimum one. Thank you or you help.

[Torsten]

1. Plot (phi-beta) vs. t1. This will give you a good initial guess for t1 such that (phi-beta)=0.

2. Use MATLAB's "fzero" together with the initial guess from 1. to approximate the zero in question with higher precision.

Don't use symbolic algebra for this problem because an analytical solution for your equation is not available.

Best wishes

Torsten.

Answer 1

[John D'Errico]

This is a 1-variable problem, but one for which there will surely be no analytical solution. Solve told you as much.

So just use fzero. Since you expect multiple solutions, just plot it, then choose a starting bracket that will yield the minimum solution. There is no need to use syms anyway if you are working with doubles. If you insist on a high precision solution, then use vpasolve, in a similar way to ensure the minimum solution.