{"id":3986,"date":"2021-08-12T12:04:31","date_gmt":"2021-08-12T12:04:31","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3986"},"modified":"2022-01-28T02:02:44","modified_gmt":"2022-01-27T20:32:44","slug":"what-is-a-periodic-function","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-a-periodic-function\/","title":{"rendered":"What is a Periodic Function – Definition and Example"},"content":{"rendered":"

Here, you will learn what is a periodic function with definition and example.<\/p>\n

Let’s begin –<\/p>\n

Periodic Function<\/h2>\n

A function f(x) is called periodic if there exist a positive number T (T > 0), where T is the smallest such value called the period of the function such that f(x + T) = f(x), for all values of x, x + T within the domain of f.<\/p>\n

Note<\/strong> :<\/p>\n

\n

(i)\u00a0 Odd powers of sinx, cosx, secx, cosecx are periodic with period 2\\(\\pi\\).<\/p>\n

(ii)\u00a0 None zero integral powers of tanx, cotx are periodic with period \\(\\pi\\).<\/p>\n

(iii)\u00a0 Non zero even powers or modulus of sinx, cosx, secx, cosecx are periodic \\(\\pi\\).<\/p>\n

(iv)\u00a0 f(T) = f(0) = f(-T), where ‘T’ is the period.<\/p>\n

(v)\u00a0 if f(x) has period T then f(ax + b) has a period T\/|a| (a \\(\\ne\\) 0).<\/p>\n

(vi)\u00a0 If f(x) & g(x) are periodic with period \\(T_1\\) & \\(T_2\\) respectively, then period of f(x) \\(\\pm\\) g(x) is L.C.M of (\\(T_1\\), \\(T_2\\))<\/p>\n

(vii)\u00a0 Every constant function is always periodic.<\/p>\n

(viii)\u00a0 Inverse of a periodic functions does not exist.<\/p>\n<\/blockquote>\n\n\n

Example : <\/span>Find the periods of the function f(x) = \\(e^{ln(sinx)}\\) + \\(tan^3x\\) – cosec(3x – 5)<\/p>\n

Solution : <\/span>Period of \\(e^{ln(sinx)}\\) = \\(2\\pi\\), \\(tan^3x\\) = \\(\\pi\\)

\n cosec(3x – 5) = \\(2\\pi\\over 3\\)

\n \\(\\therefore\\)   Period = \\(2\\pi\\)

\n <\/p>\n\n\n\n

\n
Next – What is Inverse of a Function<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – One One and Onto Function (Bijection)<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here, you will learn what is a periodic function with definition and example. Let’s begin – Periodic Function A function f(x) is called periodic if there exist a positive number T (T > 0), where T is the smallest such value called the period of the function such that f(x + T) = f(x), for …<\/p>\n

What is a Periodic Function – Definition and Example<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[26],"tags":[359,363,364],"yoast_head":"\nWhat is a Periodic Function - Definition and Example - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post, you will learn what is a periodic function with definition and example and composite function.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/what-is-a-periodic-function\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is a Periodic Function - 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