trigonometrisch

Trigonometrisch is an adjective used in German to denote things related to trigonometry, the branch of mathematics that studies the relationships between the angles and sides of triangles and the functions that express these relationships. The core ideas are the trigonometric functions sine, cosine, tangent and their reciprocal functions cosecant, secant and cotangent. These functions can be defined for real angles either via right triangles or using the unit circle in the Cartesian plane. They are periodic, with period 2π, and form the basis for identities, transformations and solving triangles.

The term originates from Greek: trigōn meaning triangle and metron meaning measure; the modern form Trigonometrie entered European mathematical language in the 17th–18th centuries. In German, trigonometrisch is used to describe methods, problems, or models that rely on trigonometry, such as trigonometrische Funktionen, trigonometrische Identitäten or trigonometrische Anwendungen in physics, engineering, astronomy and surveying.

Applications include determining unknown sides or angles in triangles, analyzing periodic phenomena, and modeling waves and rotations in physics and computer graphics. Common topics labeled trigonometrisch include the unit circle, addition and subtraction formulas, doubles and half-angles, inverse trigonometric functions, and numerical methods for evaluating trigonometric expressions. In practice, calculations are often performed in radians to maintain consistency with calculus.