Simple trigonometric proof for the new parameters of the sigma meson

Correctness of the results obtained in the recent analysis of the ππ interactions using new dispersion relations with imposed crossing symmetry condition is checked. The performed proof is based on purely mathematical relations and properties of analytic functions and concerns position of the scalar-isoscalar ƒ0(500) (former σ) pole. Mere analysis of amplitudes expressed by the trigonometric functions and their derivatives clearly defines the area in which mass of the σ and its width must be located