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Cosine Meaning: Definition, Examples, and Translations

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cosine

[ˈkɒs aɪn ]

Definitions

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

To see the translation, please select a language from the options available.

Interesting Facts

Mathematics

  • Cosine is one of the primary functions in trigonometry, alongside sine and tangent, used to relate angles to side lengths.
  • Cosine is defined in a right triangle as the ratio of the length of the adjacent side to the hypotenuse.
  • This function is periodic, meaning it repeats its values in regular intervals, specifically every 360 degrees or 2π radians.

Applications

  • Cosine is crucial in physics for analyzing wave patterns, like sound waves and light waves, helping us understand how they travel.
  • In engineering, cosine functions help design structures by ensuring stability and addressing forces acting at various angles.
  • Cosine is also widely used in computer graphics to create realistic animations and 3D models by representing rotations.

History

  • The development of cosine is closely tied to the work of ancient Greek astronomers who needed it for celestial navigation.
  • The invention of the cosine table in the 15th century revolutionized how mathematicians computed values without calculators.
  • Renowned mathematicians like Ptolemy contributed to early trigonometric concepts that eventually led to the understanding of cosine.

Pop Culture

  • In music, the concept of harmony can be explored through cosine functions which model sound frequencies and pitches.
  • Video games often use trigonometric functions, including cosine, to determine how characters move and interact with their environment.
  • There are humorously themed memes about math terms like cosine, often depicting math struggles or triumphs in an entertaining way.

Origin of 'cosine'

Main points about word origin

  • The word 'cosine' comes from the Latin 'cosinus', which means 'sine of the complement'.
  • It was introduced in the 16th century by mathematics and astronomy scholars, making the concept more accessible.
  • The prefix 'co-' stands for 'complementary', as the cosine of an angle is related to the sine of its complementary angle.

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.