der Sinus
sine
A trigonometric function that describes, in a right triangle, the ratio of the length of the opposite side to the length of the hypotenuse.
Der Sinus von 30 Grad ist exakt 0,5.
The sine of 30 degrees is exactly 0.5.

sine / sinus
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sine
A trigonometric function that describes, in a right triangle, the ratio of the length of the opposite side to the length of the hypotenuse.
Der Sinus von 30 Grad ist exakt 0,5.
The sine of 30 degrees is exactly 0.5.

You can recognize the meaning of 'Sinus' (sine / sinus) from the context. In mathematics, you will hear words like 'Winkel' (angle), 'Grad' (degree), or 'Cosinus' (cosine). In medicine, you will hear words like 'Entzündung' (inflammation), 'Nase' (nose), or 'Arzt' (doctor).
Für die Prüfung müssen wir Sinus und Cosinus berechnen können.
For the exam, we need to be able to calculate sine and cosine.
In mathematics, 'Sinus' (sine) is almost always used with the preposition 'von' (of) and a degree or angle specification. A typical construction is 'der Sinus von [Zahl] Grad' (the sine of [number] degrees).
Kannst du mir erklären, wie man den Sinus von 45 Grad berechnet?
Can you explain to me how to calculate the sine of 45 degrees?
In a medical context, 'Sinus' (sinus) is often used in the plural ('die Sinus') when referring to the paranasal sinuses. Common combinations are 'eine Entzündung der Sinus' (an inflammation of the sinuses) or 'verstopfte Sinus' (blocked sinuses).
Im Winter haben viele Menschen Probleme mit trockenen oder verstopften Sinus.
In winter, many people have problems with dry or blocked sinuses.
cavity
'Sinus' and 'Hohlraum' can both mean an empty or fluid-filled space in a structure, especially in anatomy. 'Hohlraum' is the more general word and fits many empty spaces in bodies, walls, or other solid things. 'Sinus' is more specific and technical. In medicine, it refers to certain cavities or channels, for example the paranasal sinuses. When speaking generally about an empty space, 'Hohlraum' is more natural. When a specific anatomical area is meant, 'Sinus' can be more precise.

Der Arzt erklärte, dass ein entzündeter Sinus starke Kopfschmerzen verursachen kann.
The doctor explained that an inflamed sinus can cause severe headaches.
Hinter der alten Wand entdeckten die Handwerker einen kleinen Hohlraum.
The workers discovered a small cavity behind the old wall.