Cosine: meaning, definitions and examples

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cosine

[ ˈkɒs aɪn ]

Noun

^{Context #1 | Noun}

mathematics function

Cosine is a fundamental trigonometric function defined for a right triangle as the ratio of the length of the adjacent side to the hypotenuse. In the unit circle, it represents the x-coordinate of a point at a given angle. The cosine function is periodic, with a period of 2π, and is commonly used in various applications including physics, engineering, and navigation. The graph of the cosine function is a wave that oscillates between 1 and -1.

Synonyms

cos, cosine function.

Examples of usage

The cosine of 60 degrees is 0.5.
To solve the triangle, we need to calculate the cosine of angle A.
In the equation for wave motion, cosine describes the displacement from the midpoint.

^{Context #2 | Noun}

angle measurement

In the context of angle measurement, the cosine can be used to calculate angles in various geometrical shapes. It is integral in solving triangles and can help determine unknown sides or angles. This function is essential in navigation, as it aids in calculating distances over the earth's surface.

Synonyms

cosine ratio.

Examples of usage

Using the cosine rule, we can find the length of the third side.
The cosine of 45 degrees is equal to the sine of 45 degrees.
Engineers often rely on cosine functions to model forces in structures.

Translations

Translations of the word "cosine" in other languages:

🇵🇹 cosseno

🇮🇳 कोसाइन

🇩🇪 Kosinus

🇮🇩 kosinus

🇺🇦 косинус

🇵🇱 cosinus

🇯🇵 コサイン

🇫🇷 cosinus

🇪🇸 coseno

🇹🇷 kosinüs

🇰🇷 코사인

🇸🇦 جيب التمام

🇨🇿 kosinus

🇸🇰 kosinus

🇨🇳 余弦

🇸🇮 kosinus

🇮🇸 kósínus

🇰🇿 косинус

🇬🇪 კოსინუსი

🇦🇿 kosinus

🇲🇽 coseno

Etymology

The word 'cosine' originates from the Latin term 'cosinus', which is a combination of the prefix 'co-' (meaning 'complement') and 'sinus' (meaning 'sine'). The term was first used in the 16th century when the field of trigonometry began to develop significantly in Europe. Before the term 'cosine' was adopted, the concept was described using different terminologies that highlighted the relationship between sine and the complement of angles. The formalization of trigonometric functions during this time was influenced by the work of mathematicians like Hipparchus, Ptolemy, and later Renaissance scholars who sought to understand and quantify the geometrical properties of angles and triangles. Over time, the term 'cosine' became standardized in mathematical lexicons worldwide.

Word Frequency Rank

With rank #18,532, this word belongs to specialized vocabulary. While not common in everyday speech, it enriches your ability to express complex ideas.

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18530 bracelets
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