Noun phrase
/kəʊˈsaɪn siːriz ɪkˈspænʃən/
The term cosine-series expansion refers to a mathematical technique used to express a function as a sum of cosine functions. This formulation is particularly useful in the fields of Fourier analysis and signal processing, allowing for the decomposition of periodic functions into their constituent frequencies.
In terms of frequency of use, this term is predominantly found in written contexts related to mathematics, engineering, and physics, particularly in academic papers, textbooks, and technical documentation. Its use in everyday oral speech is considerably less common.
The cosine-series expansion provides a way to approximate complex waveforms.
Расширение косинусо́вого ряда даёт возможность приближать сложные формы волн.
Many engineers rely on the cosine-series expansion to analyze periodic signals.
Многие инженеры полагаются на расширение косинусо́вого ряда для анализа периодических сигналов.
Using a cosine-series expansion can simplify the calculations in waveform synthesis.
Использование расширения косинусо́вого ряда может упростить вычисления в синтезе форма́ции.
The phrase cosine-series expansion is not commonly found in idiomatic expressions. However, the concepts of trigonometry and series can be integrated into other academic phrases or terminologies. Below are a few example sentences related to trigonometric and mathematical idioms:
In engineering, we often rely on Fourier series to bridge the gap between time domains and frequency domains.
В инженерии мы часто полагаемся на ряд Фурье, чтобы преодолеть разрыв между временными и частотными спектрами.
By transforming our approach with a series expansion, we can see the underlying patterns in the data.
Изменив наш подход с помощью разложения ряда, мы можем увидеть скрытые закономерности в данных.
A Taylor series often paves the way for understanding the behavior of functions.
Ряд Тейлора часто прокладывает путь к пониманию поведения функций.
The term cosine stems from the Latin word "cosinus," which means "complementary sine." It was first introduced in the 16th century. Series derives from the Latin "series," meaning "a row" or "a sequence." Expansion comes from the Latin "expansio," meaning "a spreading out."
Synonyms: - Fourier series - Trigonometric series - Functional expansion
Antonyms: - Contraction (in terms of reducing terms) - Simplification (as opposed to expanding functions)
This organized and detailed information provides clarity regarding the term "cosine-series expansion," its context, use, and related concepts.