sinüs

Sinüs is a term used in several languages that can refer to two main concepts: the trigonometric sine function and anatomical cavities in the body known as sinuses.

In mathematics, the sine function, usually written sin(x), assigns to each angle x the ratio of the length of the opposite side to the hypotenuse in a right triangle. On the unit circle, sin(x) corresponds to the y-coordinate of the point (cos x, sin x). The sine function is periodic with period 2π, continuous, and takes values between -1 and 1. It is an odd function, meaning sin(-x) = -sin(x). Its derivative is cos(x) and its integral is -cos(x) + C. Common identities include sin^2 x + cos^2 x = 1, sin(x + y) = sin x cos y + cos x sin y, and sin(2x) = 2 sin x cos x. The function plays a central role in trigonometry, Fourier analysis, signal processing, and many applied sciences.

Anatomical sinuses are air-filled cavities within the bones of the skull and face. The main paranasal sinuses are the maxillary, frontal, ethmoidal, and sphenoidal sinuses. They are lined with mucous membranes and connect to the nasal cavity via narrow openings (ostia). Functions attributed to the sinuses include reducing skull weight, humidifying and warming inhaled air, and contributing to voice resonance and immune defense. They can become inflamed or blocked, leading to conditions such as sinusitis, polyps, or mucocoeles, and are commonly evaluated with imaging techniques like X-ray or computed tomography.

In summary, sinüs can denote either the sine function in mathematics or the anatomical cavities in the skull and face, depending on context.