solve an equation with a given value

Question

I'm trying to solve the following equation for the value of t, but either my computer is too slow or the function is too sophisticated. The cell bar on the right side is just black and the program doesn't solve it. The equation is:

NSolve[-(95/528)
  E^(-(-0.3 + 1.5 Cos[(\[Pi] t)/3])^2 - (-1.3 + 
   1.1 Sin[(\[Pi] t)/3])^2) (Pi (-0.3 + 
     1.5 Cos[(\[Pi] t)/3]) Sin[(\[Pi] t)/3] - 
  2.303834612632515 Cos[(\[Pi] t)/
    3] (-1.3 + 1.1 Sin[(\[Pi] t)/3])) - 

0.4583333333333333 E^(-1.21 ((1.5 + 1.5 Cos[([Pi] t)/3])^2 + (-1.1 + 1.1 Sin[([Pi] t)/3])^2)) (-Pi (1.5 + 1.5 Cos[([Pi] t)/3]) Sin[([Pi] t)/3] + 2.303834612632515 Cos[([Pi] t)/ 3] (-1.1 + 1.1 Sin[([Pi] t)/3])) - 50/33 E^(-4 ((-2 + 1.5 Cos[([Pi] t)/3])^2 + (0.9 + 1.1 Sin[([Pi] t)/3])^2)) (-Pi (-2 + 1.5 Cos[([Pi] t)/3]) Sin[([Pi] t)/3] + 2.303834612632515 Cos[([Pi] t)/ 3] (0.9 + 1.1 Sin[([Pi] t)/3])) - ( 25 (-Pi (-1.75 + 1.5 Cos[([Pi] t)/3]) Sin[([Pi] t)/3] + 2.303834612632515 Cos[([Pi] t)/ 3] (-1.7 + 1.1 Sin[([Pi] t)/3])))/( 33 (1 + 4 ((-1.75 + 1.5 Cos[([Pi] t)/3])^2 + (-1.7 + 1.1 Sin[([Pi] t)/3])^2))^(3/2)) + ( 0.004734848484848485 (-Pi (-0.25 + 1.5 Cos[([Pi] t)/3]) Sin[([Pi] t)/3] + 2.303834612632515 Cos[([Pi] t)/ 3] (-1.35 + 1.1 Sin[([Pi] t)/3])))/Sqrt[ 1 + 0.25 ((-0.25 + 1.5 Cos[([Pi] t)/3])^2 + (-1.35 + 1.1 Sin[([Pi] t)/3])^2)] - ( 0.34375 (-Pi (-0.5 + 1.5 Cos[([Pi] t)/3]) Sin[([Pi] t)/3] + 2.303834612632515 Cos[([Pi] t)/ 3] (0.4 + 1.1 Sin[([Pi] t)/3])))/(1 + 1.21 ((-0.5 + 1.5 Cos[([Pi] t)/3])^2 + (0.4 + 1.1 Sin[([Pi] t)/ 3])^2))^2 - (0.42613636363636365 (-Pi (1.5 Cos[([Pi] t)/ 3]) Sin[([Pi] t)/3] + 2.303834612632515 Cos[([Pi] t)/ 3] (0.6 + 1.1 Sin[([Pi] t)/3])))/(1 + 2.25 ((1.5 Cos[([Pi] t)/3])^2 + (0.6 + 1.1 Sin[([Pi] t)/3])^2))^2 - ( 1.196496212121212 (-Pi (1.5 + 1.5 Cos[([Pi] t)/3]) Sin[([Pi] t)/ 3] + 2.303834612632515 Cos[([Pi] t)/ 3] (1.4 + 1.1 Sin[([Pi] t)/3])))/(1 + 3.61 ((1.5 + 1.5 Cos[([Pi] t)/3])^2 + (1.4 + 1.1 Sin[([Pi] t)/3])^2))^(3/2) == 0, t]

Did i do something wrong?

Answer 1

First of all, there are syntax errors : you have a bunch of [Pi] instead of backslash[Pi].

The second problem is that there are infinite number of roots. Considering the positive roots, looking at the graph, the very first are located close to $1.4$, $2.4$, $3.0$, and $4.0$.

Using FindRoot[ ], there is no problem and the solutions are $1.35296$, $2.40320$, $3.08573$ and $3.88337$.