{"id":9128,"date":"2021-12-29T17:09:57","date_gmt":"2021-12-29T11:39:57","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9128"},"modified":"2021-12-29T17:22:13","modified_gmt":"2021-12-29T11:52:13","slug":"what-is-the-value-of-cos-45-degrees","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-value-of-cos-45-degrees\/","title":{"rendered":"What is the Value of Cos 45 Degrees ?"},"content":{"rendered":"

Solution :<\/h2>\n

The value of cos 45 degrees<\/strong> is \\(1\\over \\sqrt{2}\\)<\/strong>.<\/p>\n

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

Let ABC be a triangle, right angled at B, in which \\(\\angle\\) A = \\(\\angle\\) C = 45 degrees\"45<\/p>\n

\\(\\therefore\\)  BC = AB<\/p>\n

Let  AB = BC = a<\/p>\n

Then by pythagoras theorem,<\/p>\n

\\(AC^2\\) = \\(AB^2\\) + \\(BC^2\\) = \\(a^2\\) + \\(a^2\\) = \\(2a^2\\)<\/p>\n

\\(\\implies\\)  AC = \\(\\sqrt{2}a\\)<\/p>\n

In \\(\\Delta\\) ABC,  \\(\\angle\\) C = 45 degrees<\/p>\n

By using trigonometric formulas<\/a>,<\/p>\n

\\(cos 45^{\\circ}\\) = \\(base\\over hypotenuse\\) = \\(b\\over h\\)<\/p>\n

\\(cos 45^{\\circ}\\)  = side adjacent to 45 degrees\/hypotenuse = \\(BC\\over AC\\) = \\(a\\over \\sqrt{2}a\\) = \\(1\\over \\sqrt{2}\\)<\/p>\n

Hence, the value of \\(cos 45^{\\circ}\\) = \\(1\\over \\sqrt{2}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : The value of cos 45 degrees is \\(1\\over \\sqrt{2}\\). Proof : Let ABC be a triangle, right angled at B, in which \\(\\angle\\) A = \\(\\angle\\) C = 45 degrees \\(\\therefore\\)  BC = AB Let  AB = BC = a Then by pythagoras theorem, \\(AC^2\\) = \\(AB^2\\) + \\(BC^2\\) = \\(a^2\\) + \\(a^2\\) …<\/p>\n

What is the Value of Cos 45 Degrees ?<\/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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,60],"tags":[],"yoast_head":"\nWhat is the Value of Cos 45 Degrees ? - Mathemerize<\/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\/what-is-the-value-of-cos-45-degrees\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the Value of Cos 45 Degrees ? - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : The value of cos 45 degrees is (1over sqrt{2}). 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