Finding the Values of Trigonometric Function without the Use of Scientific Calculators: The Case of Tangent Function

Abstract

In the realm of calculating trigonometric functions, computing the tangent function with a high degree of accuracy and precision without using scientific calculators has been an area of interest and importance. However, the manual determination of trigonometric values presents a formidable challenge, demanding careful attention to detail and the application of rigorous techniques. In this article, a set of formulas that enable the computation of tangent function values without resorting to scientific calculators are presented. The proposed formulas generate results that exhibit a remarkably high level of accuracy and precision, reproducible up to three decimal places. They are applicable within the degree intervals of 0 -21o, 21-45o and 45-90o. For angles larger than 90 degrees, the unit circle definition of the function was utilized. The paper provides detailed and comprehensive mathematical derivations for each formula corresponding to their respective intervals and conducts a thorough comparison of the obtained results with the pre-existing tangent function values through the utilization of a tabular method of comparison. Considering the high degree of accuracy and precision exhibited by these formulas, their practical adoption by both students and teachers at all levels of academic pursuits are recommended. Overall, the formulas proposed have the potential to facilitate mathematical calculations and scientific research by providing more accurate and efficient means of calculating tangent function values.