{"id":362,"date":"2023-07-04T14:44:12","date_gmt":"2023-07-04T14:44:12","guid":{"rendered":"https:\/\/mathority.org\/id\/periodisitas-suatu-masa-jabatan\/"},"modified":"2023-07-04T14:44:12","modified_gmt":"2023-07-04T14:44:12","slug":"periodisitas-suatu-masa-jabatan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/periodisitas-suatu-masa-jabatan\/","title":{"rendered":"Periodisitas suatu fungsi (periode)"},"content":{"rendered":"<p>Pada artikel ini kami menjelaskan apa itu periodisitas suatu fungsi. Selain itu, Anda akan melihat beberapa contoh fungsi periodik. Terakhir, kita akan menganalisis periode fungsi trigonometri, karena ini adalah salah satu karakteristik terpentingnya. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-periodicidad-de-una-funcion\"><\/span> Berapa periodisitas suatu fungsi?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Periodisitas suatu fungsi merupakan ciri dari fungsi yang berulang nilainya secara siklis, yaitu suatu fungsi bersifat periodik jika grafiknya berulang pada setiap interval tertentu. Interval ini disebut periode.<\/strong> <\/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\/periodicite-dune-fonction.webp\" alt=\"Periodisitas suatu fungsi\" class=\"wp-image-328\" width=\"348\" height=\"249\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Secara matematis, suatu fungsi dikatakan periodik jika fungsi tersebut dipenuhi saja<\/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-a459750e9149a1753a7173d6e0761e95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=f(x+T)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<p> untuk setiap nilai variabel bebas x.<\/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-762d2702efece63b455dc96e3ca7366c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=f(x+T)=f(x+2T)=f(x+3T)=\\ldots=f(x+kT)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"476\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dimana <em>T<\/em> adalah periode fungsi periodik i <em>k<\/em> bilangan bulat. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-periodicidades-de-funciones\"><\/span> Contoh periodisitas fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita melihat konsep periodisitas suatu fungsi, kita akan melihat beberapa contoh cara menghitung periodisitas suatu fungsi.<\/p>\n<h3 class=\"wp-block-heading\"> Contoh 1<\/h3>\n<p> Tentukan apakah fungsi berikut ini periodik: <\/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\/exemple-de-fonction-periodique.webp\" alt=\"contoh fungsi periodik\" class=\"wp-image-331\" width=\"636\" height=\"234\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Fungsi yang ditentukan sedikit demi sedikit ini adalah fungsi periodik, karena nilai grafiknya berulang secara siklis. Lebih tepatnya, fungsi tersebut mengambil nilai yang sama setiap enam x, sehingga periode fungsi tersebut sama dengan 6.<\/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-73bf76dfe01364f5d6e7696a532ce649_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T=6\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"45\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Contoh 2<\/h3>\n<p> Temukan periodisitas fungsi berikut: <\/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\/fonction-graphique-cosinus.webp\" alt=\"\" class=\"wp-image-293\" width=\"742\" height=\"207\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Fungsi ini sesuai dengan representasi grafis dari fungsi trigonometri, lebih tepatnya fungsi kosinus.<\/p>\n<p> Seperti dapat kita lihat dari grafik, fungsi tersebut mengulangi nilainya secara berkala, sehingga merupakan fungsi periodik. Selain itu, antara puncak dan puncak gelombang terdapat jarak 2\u03c0 (atau 360\u00ba), jadi inilah periode fungsinya. <\/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-e276a686cc8bb006030ce506a388e708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T=2\\pi\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"periodicidad-de-funciones-trigonometricas\"><\/span> Periodisitas fungsi trigonometri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Periodisitas dan fungsi trigonometri berkaitan erat, bahkan salah satu ciri utama fungsi jenis ini adalah sebagian besar fungsi trigonometri bersifat periodik.<\/p>\n<p> Selanjutnya kita akan mempelajari periodisitas 3 fungsi trigonometri utama: sinus, kosinus, dan tangen.<\/p>\n<h3 class=\"wp-block-heading\"> Periode fungsi sinus<\/h3>\n<p> Ekspresi fungsi sinus adalah sebagai berikut:<\/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-3ef34795a3bfccbfb3b0219ab0ddc3b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= A\\text{sen}(wx)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"132\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam hal ini, fungsi tersebut tidak perlu dibuat grafiknya untuk mencari periodenya, tetapi dapat dihitung hanya dengan menggunakan rumus berikut:<\/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-e76a82833c0a1d358166343d2e82e4d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle T=\\cfrac{2\\pi}{w}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"58\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Selain itu, fungsi sinus memiliki kekhasan yaitu jika kita mengubah periodenya, kita juga mengubah bentuk grafiknya. Anda dapat melihat bagaimana nilai periode mempengaruhi representasi grafisnya di tautan berikut:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/fungsi-sinus\/\">Grafik fungsi sinus<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"> Periode fungsi kosinus<\/h3>\n<p> Ekspresi aljabar untuk fungsi kosinus adalah sebagai berikut:<\/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-5d7700fc10f642ba455e6ed144d6d920_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= A\\text{cos}(wx)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Seperti halnya sinus, periode fungsi kosinus dapat dicari secara langsung dengan menggunakan rumus berikut:<\/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-e76a82833c0a1d358166343d2e82e4d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle T=\\cfrac{2\\pi}{w}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"58\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Nilai periode kosinus sepenuhnya menentukan grafiknya, klik link berikut dan cari tahu alasannya:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/fungsi-sinus\/\">Grafik fungsi kosinus<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"> Periode fungsi tangen<\/h3>\n<p> Fungsi tangen dijelaskan secara matematis:<\/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-e5e2cc1f194f1a7fee12fa1156ad3fa6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\text{tg}(wx)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Periode fungsi tangen dihitung dengan rumus yang sama seperti sinus dan kosinus:<\/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-e76a82833c0a1d358166343d2e82e4d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle T=\\cfrac{2\\pi}{w}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"58\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Namun grafik fungsi tangen berbeda dengan sinus dan kosinus karena juga mempunyai asimtot yang berulang secara berkala. Anda dapat melihat fitur ini dan fitur lainnya dari fungsi trigonometri ini di link berikut:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/fungsi-tangen\/\">Grafik fungsi tangen<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel ini kami menjelaskan apa itu periodisitas suatu fungsi. Selain itu, Anda akan melihat beberapa contoh fungsi periodik. Terakhir, kita akan menganalisis periode fungsi trigonometri, karena ini adalah salah satu karakteristik terpentingnya. Berapa periodisitas suatu fungsi? Periodisitas suatu fungsi merupakan ciri dari fungsi yang berulang nilainya secara siklis, yaitu suatu fungsi bersifat periodik jika &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/periodisitas-suatu-masa-jabatan\/\"> <span class=\"screen-reader-text\">Periodisitas suatu fungsi (periode)<\/span> Selengkapnya &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":[49],"tags":[],"class_list":["post-362","post","type-post","status-publish","format-standard","hentry","category-representasi-fungsi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Periodisitas suatu fungsi (periode)<\/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\/id\/periodisitas-suatu-masa-jabatan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Periodisitas suatu fungsi (periode)\" \/>\n<meta property=\"og:description\" content=\"Pada artikel ini kami menjelaskan apa itu periodisitas suatu fungsi. Selain itu, Anda akan melihat beberapa contoh fungsi periodik. Terakhir, kita akan menganalisis periode fungsi trigonometri, karena ini adalah salah satu karakteristik terpentingnya. Berapa periodisitas suatu fungsi? Periodisitas suatu fungsi merupakan ciri dari fungsi yang berulang nilainya secara siklis, yaitu suatu fungsi bersifat periodik jika &hellip; Periodisitas suatu fungsi (periode) Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/periodisitas-suatu-masa-jabatan\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-04T14:44:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/periodicite-dune-fonction.webp\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 menit\" \/>\n<script type=\"application\/ld+json\" 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Periodisitas suatu fungsi merupakan ciri dari fungsi yang berulang nilainya secara siklis, yaitu suatu fungsi bersifat periodik jika &hellip; Periodisitas suatu fungsi (periode) Selengkapnya &raquo;","og_url":"https:\/\/mathority.org\/id\/periodisitas-suatu-masa-jabatan\/","article_published_time":"2023-07-04T14:44:12+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/periodicite-dune-fonction.webp"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"2 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/periodisitas-suatu-masa-jabatan\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/periodisitas-suatu-masa-jabatan\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Periodisitas suatu fungsi 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