Four trigonometric identities—the sine sum, cosine sum, tangent sum, and cotangent sum—are fundamental formulas in Precalculus. They play an important role in students’ learning of mathematics and other STEM subjects. Traditionally, students memorize these formulas without fully understanding the logic behind them. As a result, they often struggle with these basic identities and related concepts.

In this paper, pictorial proofs of the four identities are presented to illustrate the reasoning behind each formula. The proofs are simple and straightforward, allowing students to visually grasp why the formulas work. This visual approach helps students more easily remember the fundamental identities and apply them to derive related formulas, leading to greater success in Precalculus and other mathematics courses.

This instructional innovation has been implemented for several years by the author in Precalculus courses at Kennesaw State University. It has had a significant positive impact on student learning, as evidenced by consistently high success rates.

Keywords: Sine Sum Identity, Cosine Sum Identity, Tagent Sum Identity, Cotegent Identity.