In the field of modern mathematics, the 60 ° angle trisecting problem has long been a classic geometric problem that has attracted much attention, and its essence is closely related to the infinite extension of trigonometric functions in the generalized dimension. Through in-depth research, it was found that the solution to this problem exists within the two-thirds interval between r and r, where r corresponds to the shape of a curve and two-thirds of r corresponds to the shape of a horizontal straight line. This article explores the inherent connections between geometric shapes from an innovative perspective and successfully constructs a new method for accurately dividing 60 ° angles into three equal parts. This method not only breaks through the limitations of traditional geometric thinking, but also has a high degree of scalability, which can be effectively extended to the problem of trisecting at any angle less than 180 ° within the two-thirds interval of r and r. It provides a new idea and solution paradigm for the theory and practical application of angle trisecting, and is expected to promote further development in related fields.