New Formulas for the Trigonometry of Isosceles Triangles

Abstract This paper discusses a new formula to solve for the angle of isosceles triangles given proportion of differentiated unequivalent edge length versus the always-equivalent edges. The equation is equal to the arcsine of (X/2) multiplied by two. This formula is to be called ‘isn^-1(x)’, short for inverse isosceles sine equivalent. Also discussed is the non-inverse ‘isn(x)’ which is the cyclic function which is determined to correspond as the equivalent of the classic sine formula to isosceles triangles. The formula set is clearly superior and powerful at calculating the angle and measure of any given obtuse or acute triangle of an unclassified type, as well as unifying a simplest-fit formula across all types of triangle. Also discussed are two transform approximation formulas, which help to analyze graphs and samples. Finally, other methods your author has obtained to calculate angles are discussed and disproven in their effectiveness against this article’s formulas at focus, as with any other known angle formulas.