Funcţie trigonometrică

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All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O.

În matematică, prin funcţii trigonometrice se înţeleg nişte funcţii ale unui unghi oarecare. They are important when studying triangles and modeling periodic phenomena, among many other applications. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to positive and negative values and even to complex numbers. All of these approaches will be presented below.

The study of trigonometric functions dates back to Babylonian times, and a considerable amount of fundamental work was done by Persian and Greek mathematicians.

In modern usage, there are six basic trigonometric functions, which are tabulated below along with equations relating them to one another. Especially in the case of the last four, these relations are often taken as the definitions of those functions, but one can define them equally well geometrically or by other means and then derive these relations. A few other functions were common historically (and appeared in the earliest tables), but are now seldom used, such as the versine (1 − cos θ) and the exsecant (sec θ − 1). Many more relations between these functions are listed in the article about trigonometric identities.

Funcţie	Abreviere	Relaţie
Sinus	sin	$\sin \theta = \cos \left(\frac{\pi}{2} - \theta \right) \,$
Cosinus	cos	$\cos \theta = \sin \left(\frac{\pi}{2} - \theta \right)\,$
Tangentă	tg / tan	$\tan \theta = \frac{1}{\cot \theta} = \frac{\sin \theta}{\cos \theta} = \cot \left(\frac{\pi}{2} - \theta \right) \,$
Cotangentă	ctg / cot	$\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta} = \tan \left(\frac{\pi}{2} - \theta \right) \,$
Secantă	sec	$\sec \theta = \frac{1}{\cos \theta} = \csc \left(\frac{\pi}{2} - \theta \right) \,$
Cosecantă	cosec / csc	$\csc \theta =\frac{1}{\sin \theta} = \sec \left(\frac{\pi}{2} - \theta \right) \,$