Mollweide's formula in teaching trigonometry

TL;DR

This paper emphasizes the importance of Mollweide's formula in teaching trigonometry, highlighting its utility in verifying solutions and deriving related laws, and advocates for its inclusion in the curriculum.

Contribution

It revisits Mollweide's formula, demonstrates its teaching potential with classroom examples, and argues for its inclusion in trigonometry education.

Findings

Mollweide's formula effectively checks oblique triangle solutions.

Proving Mollweide's formula can be done without words.

The Law of Tangents can be derived from Mollweide's formula.

Abstract

Trigonometry is one of the topics in mathematics that the students in both high school and pre-undergraduate levels need to learn. Generally, the topic covers trigonometric functions, trigonometric equations, trigonometric identities and solving oblique triangles using the Laws of Sines and Cosines. However, when solving the oblique triangles, Mollweide's formula is most likely to be omitted from the discussion. Mollweide's formula--which exhibits a cyclical nature--is particularly useful in checking one's result after solving an oblique triangle since all six components of the triangle are involved. It is interesting to note that proving Mollweide's formula can be performed without words. Furthermore, the Law of Tangents can be derived straightforwardly from this equation. In this article, we revisit Mollweide's formula and provide classroom examples where this equation comes into alive. In addition, we suggest that this seemingly less-known equation is to be included in the mathematics syllabus on the topic of Trigonometry.