"Violent solution" usually refers to a direct, simple and rude solution in mathematics, while "trigonometric function" refers to sine, cosine, tangent and other functions. So "solving trigonometric function by violence" means solving the value of trigonometric function by direct calculation.
For a trigonometric function equation, if sin(x) is equal to 0.5, we can directly find the answer, that is, the value of x, by looking up the trigonometric function table or using a calculator. This direct search method is the "violent solution".