The Chebychev’s polynomial has vast applications in GFT. The powerful tool called convolution (Or Hadamard product), subordination techniques are used in designing the new class. In establishing the core results, derivative tests, triangle inequality and appropriate results that are existing are used. Findings:The trigonometric polynomials are applied and a class of Bi-univalent functions Pa;b;cS (l ;t ;q;q ) involving Bazilevic Sakaguchi function is derived. More over, the maximum bounds for initial coefficients and Fekete-Szego functional for the underlying class are computed. This finding opens the door to young researchers to move further with successive coefficient estimates and related research. Keywords: Bistarlike functions; Bi-Starlike Functions; Bi-Univalent Functions; Sakaguchi Type Functions; Subordination; Trigonometric Polynomials

In recent research, working on coefficient bounds is very popular and useful to deal with geometric properties of the underlying functions. In this work, two new subclasses of Sakaguchi type functions with respect to symmetric points through subordination are considered. Moreover, the initial coefficients and the sharp upper bounds for the functional $|\rho_{2k+1}-\mu \rho_{k+1}^{2}|$ corresponding to $k^{th}$ root transformation belong to the above classes are obtained and thoroughly investigated.