Introduction: In the teaching of trigonometry, in the subject of high school mathematics, presented according to the textbooks, bringing contents and forms of resolution with many difficulties and practicality for teaching students to find angle between the hands of a clock., has become a reality for millions of students and teachers around the world. Based on this reality, the teaching of basic education has undergone major transformations in its teaching structure with. Objective: To develop an equation to find the angle between two hands of a clock, to meet the difficulties faced by students and teachers of teaching mathematics in basic education, through innovative methodologies that will provide learning for students and contribution to the public school community of the Municipality of São Francisco/PB, Brazil. Methodology: To carry out this research, a sample was formed by a triple factorial involving: 4 schools, 5 teachers and 10 students, from the city of São Francisco/PB/Brazil. The public elementary schools chosen to be part of the research were: EEECI Dorgival Silveira, ECI Mestre Júlio Sarmento, ECI DR. Silva Mariz and E.E.E.F.M Celson Mariz, respectively. Conclusions: In general, the difficulties pointed out by teachers and students listed in this study are related to continuing education, the scarce literature that does not offer didactic material in favor of the development of new mathematical models that can help solve trigonometry problems with ease and speed on the part of students, and the lack of innovative methodologies for teaching trigonometry both in the eyes of teachers and students. Thus, there are many barriers in the teaching and learning of mathematics, requiring the development of new research that dynamically enables the teaching of this discipline