{"id":363,"date":"2023-07-04T13:41:37","date_gmt":"2023-07-04T13:41:37","guid":{"rendered":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/"},"modified":"2023-07-04T13:41:37","modified_gmt":"2023-07-04T13:41:37","slug":"funcao-cosseno-hiperbolica","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/","title":{"rendered":"Fun\u00e7\u00e3o cosseno hiperb\u00f3lica"},"content":{"rendered":"<p>Aqui voc\u00ea encontrar\u00e1 tudo sobre a fun\u00e7\u00e3o cosseno hiperb\u00f3lico: qual a sua f\u00f3rmula, sua representa\u00e7\u00e3o gr\u00e1fica, suas caracter\u00edsticas, as rela\u00e7\u00f5es matem\u00e1ticas com outras fun\u00e7\u00f5es, etc. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-coseno-hiperbolico\"><\/span> F\u00f3rmula hiperb\u00f3lica do cosseno<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A fun\u00e7\u00e3o <strong>cosseno hiperb\u00f3lica<\/strong> \u00e9 uma das principais fun\u00e7\u00f5es hiperb\u00f3licas e \u00e9 representada pelo s\u00edmbolo <strong>cosh(x)<\/strong> . O cosseno hiperb\u00f3lico \u00e9 igual \u00e0 soma de e <sup>x<\/sup> mais e <sup>-x<\/sup> dividido por 2.<\/p>\n<p> Portanto, a f\u00f3rmula do cosseno hiperb\u00f3lico \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f667377a7e792f2c9f5f5a7a0ecda4e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)=\\cfrac{e^{x}+e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Assim, o cosseno hiperb\u00f3lico est\u00e1 matematicamente relacionado \u00e0 fun\u00e7\u00e3o exponencial. No link a seguir voc\u00ea pode ver as propriedades deste tipo de fun\u00e7\u00e3o:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/funcao-exponencial\/\">propriedades da fun\u00e7\u00e3o exponencial<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"representacion-grafica-del-coseno-hiperbolico\"><\/span> Representa\u00e7\u00e3o gr\u00e1fica do cosseno hiperb\u00f3lico<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o cosseno hiperb\u00f3lico tem a forma de uma fun\u00e7\u00e3o quadr\u00e1tica (ou par\u00e1bola): <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/cosinus-hyperbolique.webp\" alt=\"cosseno hiperb\u00f3lico\" class=\"wp-image-376\" width=\"281\" height=\"308\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/funcao-de-parabola-quadratica\/\">Representa\u00e7\u00e3o gr\u00e1fica de uma fun\u00e7\u00e3o quadr\u00e1tica<\/a><\/span> .<\/p>\n<p> Neste gr\u00e1fico, podemos ver claramente que o cosseno hiperb\u00f3lico \u00e9 uma fun\u00e7\u00e3o par, porque \u00e9 sim\u00e9trico em rela\u00e7\u00e3o ao eixo y.<\/p>\n<p> Por outro lado, o gr\u00e1fico do cosseno hiperb\u00f3lico \u00e9 muito diferente daquele do cosseno (fun\u00e7\u00e3o trigonom\u00e9trica), que \u00e9 uma fun\u00e7\u00e3o peri\u00f3dica. Voc\u00ea pode ver a representa\u00e7\u00e3o gr\u00e1fica do cosseno e todas as diferen\u00e7as com o cosseno hiperb\u00f3lico no seguinte link:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/funcao-cosseno\/\">representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o cosseno<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-del-coseno-hiperbolico\"><\/span> Caracter\u00edsticas do cosseno hiperb\u00f3lico<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O cosseno hiperb\u00f3lico respeita as seguintes propriedades:<\/p>\n<ul>\n<li> O dom\u00ednio da fun\u00e7\u00e3o cosseno hiperb\u00f3lico s\u00e3o todos os n\u00fameros reais:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd1539b66edeb38040ed80168e1fd9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul>\n<li> Em vez disso, o intervalo (ou intervalo) da fun\u00e7\u00e3o cosseno hiperb\u00f3lica \u00e9 1 e todos os n\u00fameros maiores que 1:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60c76341385ea1ebb5f20476cd8226f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Im } f= [1,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> O cosseno hiperb\u00f3lico \u00e9 uma fun\u00e7\u00e3o cont\u00ednua e par.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91f3c4459fc8d8840fd902946c851d1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{cosh}(-x)=\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> A fun\u00e7\u00e3o intercepta o eixo Y no ponto x=0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd01415f329053c1a450867378fc1582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Por outro lado, a fun\u00e7\u00e3o n\u00e3o tem ponto de intersec\u00e7\u00e3o com o eixo X.<\/li>\n<\/ul>\n<ul>\n<li> Os dois limites ao infinito (positivo e negativo) da fun\u00e7\u00e3o cosseno hiperb\u00f3lica d\u00e3o mais infinito.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a5aadc0c48684e553e9971aefe442d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to+\\infty}\\text{cosh}(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"161\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fb2a605c43e81635473abf73554d264f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to-\\infty}\\text{cosh}(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"161\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> O cosseno hiperb\u00f3lico diminui at\u00e9 x = 0 e a partir desse ponto aumenta indefinidamente, ent\u00e3o a fun\u00e7\u00e3o tem m\u00ednimo em x = 0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd01415f329053c1a450867378fc1582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> A fun\u00e7\u00e3o \u00e9 convexa em todo o seu dom\u00ednio, portanto n\u00e3o possui ponto de inflex\u00e3o.<\/li>\n<\/ul>\n<ul>\n<li> A derivada da fun\u00e7\u00e3o cosseno hiperb\u00f3lico \u00e9 o seno hiperb\u00f3lico:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a7a982aae764353843a57652f9a6797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(x) \\ \\longrightarrow \\ f'(x)=\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"286\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> A integral da fun\u00e7\u00e3o cosseno hiperb\u00f3lico \u00e9 o seno hiperb\u00f3lico:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a509c96c515bb7115359764e7e4451df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\int \\text{cosh}(x) \\ dx= \\text{senh}(x) + C\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"221\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> O polin\u00f4mio de Taylor (ou s\u00e9rie de Maclaurin) da fun\u00e7\u00e3o cosseno hiperb\u00f3lica \u00e9 o seguinte:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdbe87b63234b62e226371256f8a6c8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)=1+\\cfrac{x^2}{2!}+\\cfrac{x^4}{4!}+\\cfrac{x^6}{6!}+\\dots=\\sum_{n=0}^\\infty\\cfrac{x^{2n}}{(2n)!}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"350\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<ul>\n<li> A transformada de Laplace da fun\u00e7\u00e3o cosseno hiperb\u00f3lica \u00e9 a seguinte: <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ee373a19450972f0c4cccc3a273770e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathcal{L}\\bigl[\\text{cosh}(at)\\bigr]=\\cfrac{s}{s^2-a^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"171\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"relaciones-matematicas-del-coseno-hiperbolico\"><\/span> Rela\u00e7\u00f5es matem\u00e1ticas do cosseno hiperb\u00f3lico<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A seguir, veremos como o cosseno hiperb\u00f3lico pode ser calculado a partir de outras fun\u00e7\u00f5es hiperb\u00f3licas, uma vez que todas est\u00e3o matematicamente relacionadas.<\/p>\n<p> A equa\u00e7\u00e3o fundamental relaciona o cosseno hiperb\u00f3lico ao seno hiperb\u00f3lico:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4317a445a90e4d139b47db7cf4a49a1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}^2(x)-\\text{senh}^2(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/mathority.org\/pt\/funcao-seno-hiperbolica\/\"><span style=\"text-decoration: underline;\">seno hiperb\u00f3lico<\/span><\/a><\/p>\n<p> As tr\u00eas principais fun\u00e7\u00f5es hiperb\u00f3licas (seno, cosseno e tangente hiperb\u00f3licos) podem ser relacionadas pela seguinte equa\u00e7\u00e3o:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-12f286528bc0635705aadbe510b6ceb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}(x)=\\cfrac{\\text{senh}(x)}{\\text{cosh}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"144\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Por outro lado, o cosseno hiperb\u00f3lico da adi\u00e7\u00e3o (ou subtra\u00e7\u00e3o) de dois n\u00fameros diferentes pode ser determinado pelas seguintes f\u00f3rmulas:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-75dff3fbdfd533e08cf581767a0d9b7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(x+y)=\\text{cosh}(x)\\text{cosh}(y)+\\text{senh}(y)\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"363\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3762e67762eecb02ed3d30c39febca9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(x-y)=\\text{cosh}(x)\\text{cosh}(y)-\\text{senh}(y)\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"363\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> O cosseno hiperb\u00f3lico de duas vezes um n\u00famero \u00e9 igual \u00e0 soma dos quadrados do cosseno hiperb\u00f3lico e do seno hiperb\u00f3lico deste n\u00famero:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-be5e2f8a1f407e6dce0c53932575d545_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(2x)=\\text{cosh}^2(x)+\\text{senh}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"242\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A adi\u00e7\u00e3o ou subtra\u00e7\u00e3o de dois cossenos hiperb\u00f3licos pode ser calculada aplicando as seguintes f\u00f3rmulas:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02b9d1c798f2639e6503add69dcdb401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)+\\text{cosh}(y)=2\\text{cosh}\\left(\\frac{x+y}{2}\\right)\\text{cosh}\\left(\\frac{x-y}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"384\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ec9d613adc720e383f1c3c0c9c8ca5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)-\\text{cosh}(y)=2\\text{senh}\\left(\\frac{x+y}{2}\\right)\\text{senh}\\left(\\frac{x-y}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"386\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Finalmente, o quadrado do cosseno hiperb\u00f3lico pode ser calculado com a seguinte f\u00f3rmula:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33c90357c8680ebd2ca5725aad7703f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}^2(x)=\\cfrac{1}{2}\\Bigl(\\text{cosh}(2x)+1\\Bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"215\" style=\"vertical-align: -12px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aqui voc\u00ea encontrar\u00e1 tudo sobre a fun\u00e7\u00e3o cosseno hiperb\u00f3lico: qual a sua f\u00f3rmula, sua representa\u00e7\u00e3o gr\u00e1fica, suas caracter\u00edsticas, as rela\u00e7\u00f5es matem\u00e1ticas com outras fun\u00e7\u00f5es, etc. F\u00f3rmula hiperb\u00f3lica do cosseno A fun\u00e7\u00e3o cosseno hiperb\u00f3lica \u00e9 uma das principais fun\u00e7\u00f5es hiperb\u00f3licas e \u00e9 representada pelo s\u00edmbolo cosh(x) . O cosseno hiperb\u00f3lico \u00e9 igual \u00e0 soma de e &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/\"> <span class=\"screen-reader-text\">Fun\u00e7\u00e3o cosseno hiperb\u00f3lica<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[22],"tags":[],"class_list":["post-363","post","type-post","status-publish","format-standard","hentry","category-representacao-de-funcao"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Fun\u00e7\u00e3o cosseno hiperb\u00f3lico - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fun\u00e7\u00e3o cosseno hiperb\u00f3lico - Mathority\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 tudo sobre a fun\u00e7\u00e3o cosseno hiperb\u00f3lico: qual a sua f\u00f3rmula, sua representa\u00e7\u00e3o gr\u00e1fica, suas caracter\u00edsticas, as rela\u00e7\u00f5es matem\u00e1ticas com outras fun\u00e7\u00f5es, etc. F\u00f3rmula hiperb\u00f3lica do cosseno A fun\u00e7\u00e3o cosseno hiperb\u00f3lica \u00e9 uma das principais fun\u00e7\u00f5es hiperb\u00f3licas e \u00e9 representada pelo s\u00edmbolo cosh(x) . O cosseno hiperb\u00f3lico \u00e9 igual \u00e0 soma de e &hellip; Fun\u00e7\u00e3o cosseno hiperb\u00f3lica Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-04T13:41:37+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f667377a7e792f2c9f5f5a7a0ecda4e9_l3.png\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Fun\u00e7\u00e3o cosseno hiperb\u00f3lica\",\"datePublished\":\"2023-07-04T13:41:37+00:00\",\"dateModified\":\"2023-07-04T13:41:37+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/\"},\"wordCount\":601,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Representa\u00e7\u00e3o de fun\u00e7\u00e3o\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/\",\"url\":\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/\",\"name\":\"Fun\u00e7\u00e3o cosseno hiperb\u00f3lico - Mathority\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/#website\"},\"datePublished\":\"2023-07-04T13:41:37+00:00\",\"dateModified\":\"2023-07-04T13:41:37+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Fun\u00e7\u00e3o cosseno hiperb\u00f3lica\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/pt\/#website\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"name\":\"Mathority\",\"description\":\"Onde a curiosidade encontra o c\u00e1lculo!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/pt\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\",\"name\":\"Equipe Mathoridade\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Equipe Mathoridade\"},\"sameAs\":[\"http:\/\/mathority.org\/pt\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Fun\u00e7\u00e3o cosseno hiperb\u00f3lico - Mathority","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/","og_locale":"pt_BR","og_type":"article","og_title":"Fun\u00e7\u00e3o cosseno hiperb\u00f3lico - Mathority","og_description":"Aqui voc\u00ea encontrar\u00e1 tudo sobre a fun\u00e7\u00e3o cosseno hiperb\u00f3lico: qual a sua f\u00f3rmula, sua representa\u00e7\u00e3o gr\u00e1fica, suas caracter\u00edsticas, as rela\u00e7\u00f5es matem\u00e1ticas com outras fun\u00e7\u00f5es, etc. F\u00f3rmula hiperb\u00f3lica do cosseno A fun\u00e7\u00e3o cosseno hiperb\u00f3lica \u00e9 uma das principais fun\u00e7\u00f5es hiperb\u00f3licas e \u00e9 representada pelo s\u00edmbolo cosh(x) . O cosseno hiperb\u00f3lico \u00e9 igual \u00e0 soma de e &hellip; Fun\u00e7\u00e3o cosseno hiperb\u00f3lica Leia mais &raquo;","og_url":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/","article_published_time":"2023-07-04T13:41:37+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f667377a7e792f2c9f5f5a7a0ecda4e9_l3.png"}],"author":"Equipe Mathoridade","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Equipe Mathoridade","Est. tempo de leitura":"3 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/"},"author":{"name":"Equipe Mathoridade","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00"},"headline":"Fun\u00e7\u00e3o cosseno hiperb\u00f3lica","datePublished":"2023-07-04T13:41:37+00:00","dateModified":"2023-07-04T13:41:37+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/"},"wordCount":601,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"articleSection":["Representa\u00e7\u00e3o de fun\u00e7\u00e3o"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/","url":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/","name":"Fun\u00e7\u00e3o cosseno hiperb\u00f3lico - Mathority","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/#website"},"datePublished":"2023-07-04T13:41:37+00:00","dateModified":"2023-07-04T13:41:37+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/pt\/funcao-cosseno-hiperbolica\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/pt\/"},{"@type":"ListItem","position":2,"name":"Fun\u00e7\u00e3o cosseno hiperb\u00f3lica"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/pt\/#website","url":"https:\/\/mathority.org\/pt\/","name":"Mathority","description":"Onde a curiosidade encontra o c\u00e1lculo!","publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/pt\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"pt-BR"},{"@type":"Organization","@id":"https:\/\/mathority.org\/pt\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/pt\/","logo":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00","name":"Equipe Mathoridade","image":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Equipe Mathoridade"},"sameAs":["http:\/\/mathority.org\/pt"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/363","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/comments?post=363"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/363\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/media?parent=363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/categories?post=363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/tags?post=363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}