Μετάφραση και ανάλυση λέξεων από την τεχνητή νοημοσύνη ChatGPT
Σε αυτήν τη σελίδα μπορείτε να λάβετε μια λεπτομερή ανάλυση μιας λέξης ή μιας φράσης, η οποία δημιουργήθηκε χρησιμοποιώντας το ChatGPT, την καλύτερη τεχνολογία τεχνητής νοημοσύνης μέχρι σήμερα:
- πώς χρησιμοποιείται η λέξη
- συχνότητα χρήσης
- χρησιμοποιείται πιο συχνά στον προφορικό ή γραπτό λόγο
- επιλογές μετάφρασης λέξεων
- παραδείγματα χρήσης (πολλές φράσεις με μετάφραση)
- ετυμολογία
logarithmic cosine - translation to ρωσικά
![proportional]].](https://commons.wikimedia.org/wiki/Special:FilePath/Academ Base of trigonometry.svg?width=200 "proportional]].")
![A [[Lissajous curve]], a figure formed with a trigonometry-based function.](https://commons.wikimedia.org/wiki/Special:FilePath/Lissajous curve 5by4.svg?width=200 "A [[Lissajous curve]], a figure formed with a trigonometry-based function.")
![k}} is large is called the [[Gibbs phenomenon]]](https://commons.wikimedia.org/wiki/Special:FilePath/Sawtooth Fourier Animation.gif?width=200 "k}} is large is called the [[Gibbs phenomenon]]")
![An animation of the [[additive synthesis]] of a [[square wave]] with an increasing number of harmonics](https://commons.wikimedia.org/wiki/Special:FilePath/Synthesis square.gif?width=200 "An animation of the [[additive synthesis]] of a [[square wave]] with an increasing number of harmonics")
![Taylor polynomial]] of degree 7 (pink) for a full cycle centered on the origin.](https://commons.wikimedia.org/wiki/Special:FilePath/Taylorsine.svg?width=200 "Taylor polynomial]] of degree 7 (pink) for a full cycle centered on the origin.")
![Cotangent (dotted)}}
– [{{filepath:trigonometric_functions_derivation_animation.svg}} animation]](https://commons.wikimedia.org/wiki/Special:FilePath/Trigonometric functions.svg?width=200 "Cotangent (dotted)}}
– [{{filepath:trigonometric_functions_derivation_animation.svg}} animation]")
![The [[unit circle]], with some points labeled with their cosine and sine (in this order), and the corresponding angles in radians and degrees.](https://commons.wikimedia.org/wiki/Special:FilePath/Unit circle angles color.svg?width=200 "The [[unit circle]], with some points labeled with their cosine and sine (in this order), and the corresponding angles in radians and degrees.")
математика
логарифм косинуса
общая лексика
логарифмическая бумага
 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg?width=200)
математика
интегральный логарифм
Ορισμός
Βικιπαίδεια
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions.
The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extend the sine and cosine functions to functions whose domain is the whole real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) are often used; then the domain of the other functions is the real line with some isolated points removed. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane with some isolated points removed.
