{"id":7974,"date":"2023-05-11T01:21:22","date_gmt":"2023-05-10T19:51:22","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=7974"},"modified":"2023-05-08T02:02:19","modified_gmt":"2023-05-07T20:32:19","slug":"how-to-draw-graph-of-sin-inverse-sin-x","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/how-to-draw-graph-of-sin-inverse-sin-x\/","title":{"rendered":"how to draw graph of sin inverse sin x"},"content":{"rendered":"\n

Here in this post ,we will check out how to draw the graph of sin inverse sin x i.e<\/p>\n\n\n\n

$f(x) = sin^{-1} sin (x)$<\/p>\n\n\n\n

We know by definition<\/p>\n\n\n\n

$f(x) = sin^{-1} sin (x) = x $ if $x \\in [-\\pi\/2, \\pi\/2]$<\/p>\n\n\n\n

Lets check out the other values<\/p>\n\n\n\n

if $x \\in (\\pi\/2, 3\\pi\/2]$<\/p>\n\n\n\n

$\\pi\/2 < x \\leq 3\\pi\/2$
$- 3\\pi\/2 \\leq -x < -\\pi\/2$
$\\pi – 3\\pi\/2 \\leq \\pi -x < \\pi – \\pi\/2$
$-\\pi\/2 \\leq \\pi -x < \\pi\/2$<\/p>\n\n\n\n

Now $Sin(\\pi -x) =sinx$<\/p>\n\n\n\n

So $f(x) = sin^{-1} sin (x) = sin^{-1} sin (\\pi -x)= \\pi -x$<\/p>\n\n\n\n

if $x \\in (3\\pi\/2, 2\\pi]$<\/p>\n\n\n\n

$3\\pi\/2 < x \\leq 2\\pi$
$3\\pi\/2 -2 \\pi < x- 2 \\pi < 0$
$-\\pi\/2 < x- 2 \\pi < 0$<\/p>\n\n\n\n

Now $sin (2\\pi -x) = -sin(x)$
or $sin(x) = sin (x -2 \\pi)$<\/p>\n\n\n\n

So $f(x) = sin^{-1} sin (x) = sin^{-1} sin (x -2 \\pi)= x- 2\\pi$<\/p>\n\n\n\n

Therefore the graph will be<\/p>\n\n\n\n

\"\"<\/a><\/figure>\n\n\n\n

Here f(x) is a periodic function with period $2 \\pi$, So same graph will be repeated for all the $2 \\pi$ intervals<\/p>\n","protected":false},"excerpt":{"rendered":"

Here in this post ,we will check out how to draw the graph of sin inverse sin x i.e $f(x) = sin^{-1} sin (x)$ We know by definition $f(x) = sin^{-1} sin (x) = x $ if $x \\in [-\\pi\/2, \\pi\/2]$ Lets check out the other values if $x \\in (\\pi\/2, 3\\pi\/2]$ $\\pi\/2 < x […]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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sin x i.e $f(x) = sin^{-1} sin (x)$ We know by definition $f(x) = sin^{-1} sin (x) = x $ if $x in [-pi\/2, pi\/2]$ Lets check out the other values if $x in (pi\/2, 3pi\/2]$ $pi\/2 < x […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/physicscatalyst.com\/article\/how-to-draw-graph-of-sin-inverse-sin-x\/\" \/>\n<meta property=\"og:site_name\" content=\"physicscatalyst's Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/PhysicsCatalyst\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/PhysicsCatalyst\" \/>\n<meta property=\"article:published_time\" content=\"2023-05-10T19:51:22+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/05\/graph-of-sin-inverse-sinx-1.png\" \/>\n<meta name=\"author\" content=\"physicscatalyst\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"physicscatalyst\" 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in this post ,we will check out how to draw the graph of sin inverse sin x i.e $f(x) = sin^{-1} sin (x)$ We know by definition $f(x) = sin^{-1} sin (x) = x $ if $x \\in [-\\pi\/2, \\pi\/2]$ Lets check out the other values if $x \\in (\\pi\/2, 3\\pi\/2]$ $\\pi\/2 < x…","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7974","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/comments?post=7974"}],"version-history":[{"count":1,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7974\/revisions"}],"predecessor-version":[{"id":7977,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7974\/revisions\/7977"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=7974"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=7974"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=7974"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}