{"id":10321,"date":"2025-07-15T13:34:50","date_gmt":"2025-07-15T13:34:50","guid":{"rendered":"https:\/\/functiontranslator.com\/cosh\/"},"modified":"2021-02-26T05:05:40","modified_gmt":"2021-02-26T05:05:40","slug":"cosh","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/pl\/cosh\/","title":{"rendered":"COSH"},"content":{"rendered":"

Wprowadzenie do obliczania cosinusa hiperbolicznego<\/h2>\n

Funkcja COSH oblicza cosinus hiperboliczny podanej liczby. Jest to funkcja dost\u0119pna zar\u00f3wno w Microsoft Excel, jak i Google Sheets, kt\u00f3re s\u0105 cz\u0119sto stosowane do analiz matematycznych i finansowych. Cosinus hiperboliczny jest u\u017cywany w r\u00f3\u017cnych dziedzinach nauki, w szczeg\u00f3lno\u015bci tam, gdzie pojawiaj\u0105 si\u0119 dzia\u0142ania zwi\u0105zane z rachunkiem r\u00f3\u017cniczkowym i ca\u0142kowym.<\/p>\n

Syntaktyka i przyk\u0142ady u\u017cycia<\/h2>\n

Podstawowa sk\u0142adnia funkcji COSH jest jednolita dla obu program\u00f3w:<\/p>\n

W Excel i Google Sheets:<\/strong> =COSH(liczba)<\/code><\/pre>\n
Gdzie liczba<\/code> to warto\u015b\u0107, dla kt\u00f3rej chcemy obliczy\u0107 cosinus hiperboliczny.<\/p>\n
Przyk\u0142ady u\u017cycia:<\/p>\n
    \n
  • =COSH(0)<\/code> zwr\u00f3ci 1, poniewa\u017c cosh(0) = 1.<\/li>\n
  • =COSH(1)<\/code> zwr\u00f3ci oko\u0142o 1.54, jest to warto\u015b\u0107 cosinus hiperbolicznego dla 1.<\/li>\n<\/ul>\n
    Praktyczne zastosowania<\/h2>\n
    Analiza wzrostu populacji<\/h3>\n
    W modelowaniu matematycznym cz\u0119sto korzysta si\u0119 z funkcji hiperbolicznych do opisania wzrostu populacji, gdzie szybko\u015b\u0107 wzrostu mo\u017cna modelowa\u0107 przy pomocy cosinusa hiperbolicznego w zale\u017cno\u015bci od czasu.<\/p>\n
    Przyk\u0142ad: Za\u0142\u00f3\u017cmy, \u017ce wzrost pewnej populacji y mo\u017cna modelowa\u0107 jako: y(t) = 100 * COSH(t \/ 10) Gdzie t to czas w latach. Mo\u017cemy obliczy\u0107 populacj\u0119 po 5 latach: =COSH(5\/10) * 100<\/code><\/pre>\n
    Formu\u0142a zwraca wynik oko\u0142o 127.63, co oznacza, \u017ce po 5 latach populacja wzro\u015bnie do oko\u0142o 128 os\u00f3b.<\/p>\n
    W obliczeniach in\u017cynieryjnych<\/h3>\n
    Funkcja COSH jest r\u00f3wnie\u017c wykorzystywana w in\u017cynierii, na przyk\u0142ad w obliczeniach zwi\u0105zanych z wychyleniem konstrukcji czy most\u00f3w pod wp\u0142ywem obci\u0105\u017cenia.<\/p>\n
    Dane: Mamy \u0142uk mostu, gdzie maksymalne ugi\u0119cie f (wychylenie od pozycji neutralnej) w \u015brodku wynosi: f(x) = f0 * COSH(x \/ l) - 1 Gdzie f0 to wychylenie maksymalne, a l to d\u0142ugo\u015b\u0107 \u0142uku. Przypu\u015b\u0107my, \u017ce f0 = 0.5m i l = 100m. Obliczymy ugi\u0119cie w punkcie x = 50m: =COSH(50\/100) * 0.5 - 1<\/code><\/pre>\n
    Wynik oko\u0142o -0.76 m wskazuje, \u017ce realne ugi\u0119cie b\u0119dzie mia\u0142o warto\u015b\u0107 oko\u0142o 76 cm poni\u017cej poziomu neutralnego.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Zwraca cosinus hiperboliczny liczby<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[423],"tags":[],"class_list":["post-10321","post","type-post","status-publish","format-standard","hentry","category-matematyczne-i-trygonometryczne"],"acf":[],"yoast_head":"\nFunkcja COSH w Excelu \u2013 jak dzia\u0142a, przyk\u0142ady u\u017cycia i sk\u0142adnia<\/title>\n<meta name=\"description\" content=\"Opis funkcji COSH w Excelu. 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