{"id":6819,"date":"2021-10-21T19:08:05","date_gmt":"2021-10-21T13:38:05","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6819"},"modified":"2021-10-25T00:23:27","modified_gmt":"2021-10-24T18:53:27","slug":"evaluate-sin-1sin10","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/","title":{"rendered":"Evaluate \\(sin^{-1}(sin10)\\)"},"content":{"rendered":"

Solution :<\/h2>\n

We know that \\(sin^{-1}(sinx)\\) = x, if \\(-\\pi\\over 2\\) \\(\\le\\) x \\(\\le\\) \\(\\pi\\over 2\\)<\/p>\n

Here, x = 10 radians which does not lie between -\\(\\pi\\over 2\\) and \\(\\pi\\over 2\\)<\/p>\n

But, \\(3\\pi\\) – x i.e. \\(3\\pi\\) – 10 lie between -\\(\\pi\\over 2\\) and \\(\\pi\\over 2\\)<\/p>\n

Also, sin(\\(3\\pi\\) – 10) = sin 10<\/p>\n

\\(\\therefore\\)\u00a0 \\(sin^{-1}(sin10)\\) = \\(sin^{-1}(sin(3\\pi – 10)\\) = (\\(3\\pi\\) – 10)<\/p>\n

\n

Similar Questions<\/h3>\n

Solve the equation : 2\\(tan^{-1}({2x+1})\\) = \\(cos^{-1}x\\)<\/a><\/p>\n

Prove that : \\(sin^{-1}{12\\over 13}\\) + \\(cot^{-1}{4\\over 3}\\) + \\(tan^{-1}{63\\over 16}\\) = \\(\\pi\\)<\/a><\/p>\n

The value of \\(tan^{-1}(1)\\) + \\(cos^{-1}({-1\\over 2})\\) + \\(sin^{-1}({-1\\over 2})\\) is equal to<\/a><\/p>\n

Prove that : \\(cos^{-1}{12\\over 13}\\) + \\(sin^{-1}{3\\over 5}\\) = \\(sin^{-1}{56\\over 65}\\)<\/a><\/p>\n

Find the value of \\(sin^{-1}({-\\sqrt{3}\\over 2})\\) + \\(cos^{-1}(cos({7\\pi\\over 6}))\\).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We know that \\(sin^{-1}(sinx)\\) = x, if \\(-\\pi\\over 2\\) \\(\\le\\) x \\(\\le\\) \\(\\pi\\over 2\\) Here, x = 10 radians which does not lie between -\\(\\pi\\over 2\\) and \\(\\pi\\over 2\\) But, \\(3\\pi\\) – x i.e. \\(3\\pi\\) – 10 lie between -\\(\\pi\\over 2\\) and \\(\\pi\\over 2\\) Also, sin(\\(3\\pi\\) – 10) = sin 10 \\(\\therefore\\)\u00a0 \\(sin^{-1}(sin10)\\) …<\/p>\n

Evaluate \\(sin^{-1}(sin10)\\)<\/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":[53,43],"tags":[],"yoast_head":"\nEvaluate \\(sin^{-1}(sin10)\\)<\/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:\/\/mathemerize.com\/evaluate-sin-1sin10\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Evaluate \\(sin^{-1}(sin10)\\)\" \/>\n<meta property=\"og:description\" content=\"Solution : We know that (sin^{-1}(sinx)) = x, if (-piover 2) (le) x (le) (piover 2) Here, x = 10 radians which does not lie between -(piover 2) and (piover 2) But, (3pi) – x i.e. (3pi) – 10 lie between -(piover 2) and (piover 2) Also, sin((3pi) – 10) = sin 10 (therefore)\u00a0 (sin^{-1}(sin10)) … Evaluate (sin^{-1}(sin10)) Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T13:38:05+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T18:53:27+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Evaluate \\\\(sin^{-1}(sin10)\\\\)\",\"datePublished\":\"2021-10-21T13:38:05+00:00\",\"dateModified\":\"2021-10-24T18:53:27+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/\"},\"wordCount\":131,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Inverse Trigonometric Function Questions\",\"Maths Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/\",\"url\":\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/\",\"name\":\"Evaluate \\\\(sin^{-1}(sin10)\\\\)\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-21T13:38:05+00:00\",\"dateModified\":\"2021-10-24T18:53:27+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/evaluate-sin-1sin10\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Evaluate \\\\(sin^{-1}(sin10)\\\\)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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