Trigonometrical

Trigonometrical is an adjective relating to trigonometry, the branch of mathematics that studies the relationships between angles and the lengths of sides in triangles. Trigonometrical methods are used to solve problems involving distances and angles, and to describe periodic phenomena through trigonometric functions such as sine, cosine, and tangent, which can be defined in right triangles or on the unit circle.

The word combines Greek roots: trigōn, meaning triangle, and metron, meaning measure. It is closely related to the noun trigonometry and to the adjective trigonometrical, both of which appear in historical and some regional texts. In modern standard English, "trigonometric" is far more common.

While function names and identities are common in both spellings, most contemporary style guides favor "trigonometric." The term "trigonometrical" is mostly encountered in older literature, British English variants, or when describing older methods and textbooks.

Historically, trigonometry developed in ancient Greek, Indian, and Islamic mathematics, expanding with European mathematicians in the Renaissance. Today, trigonometrical (or trigonometric) concepts underpin fields such as physics, engineering, computer science, astronomy, and navigation, enabling calculations of angles, distances, waveforms, and rotational motions.