{"id":9428,"date":"2022-01-13T19:30:03","date_gmt":"2022-01-13T14:00:03","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9428"},"modified":"2022-01-13T22:53:13","modified_gmt":"2022-01-13T17:23:13","slug":"what-is-the-general-solution-of-sin-theta-0","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-general-solution-of-sin-theta-0\/","title":{"rendered":"What is the General Solution of \\(Sin \\theta\\) = 0 ?"},"content":{"rendered":"

Solution :<\/h2>\n

The general solution of \\(sin \\theta\\) = 0<\/strong> is given by \\(\\theta\\) = \\(n\\pi\\), n \\(\\in\\) Z.<\/strong><\/p>\n

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

We have,\"theta\"<\/p>\n

\\(sin \\theta\\) = \\(PM\\over OP\\)<\/p>\n

\\(\\therefore\\)   \\(sin \\theta\\) = 0<\/p>\n

\\(\\implies\\)  \\(PM\\over OP\\) = 0<\/p>\n

\\(\\implies\\) PM = 0<\/p>\n

\\(\\implies\\)  OP coincides with OX or OX’<\/p>\n

\\(\\implies\\)  \\(\\theta\\) = 0, \\(\\pi\\), \\(2\\pi\\), ….., \\(-\\pi\\), \\(-2\\pi\\), \\(-3\\pi\\), ….<\/p>\n

\\(\\implies\\) \\(\\theta\\) = \\(n\\pi\\),  n \\(\\in\\) Z<\/p>\n

Hence, \\(\\theta\\) = \\(n\\pi\\),  n \\(\\in\\) Z is the general solution of \\(sin \\theta\\) = 0.<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : The general solution of \\(sin \\theta\\) = 0 is given by \\(\\theta\\) = \\(n\\pi\\), n \\(\\in\\) Z. Proof : We have, \\(sin \\theta\\) = \\(PM\\over OP\\) \\(\\therefore\\)   \\(sin \\theta\\) = 0 \\(\\implies\\)  \\(PM\\over OP\\) = 0 \\(\\implies\\) PM = 0 \\(\\implies\\)  OP coincides with OX or OX’ \\(\\implies\\)  \\(\\theta\\) = 0, \\(\\pi\\), \\(2\\pi\\), …<\/p>\n

What is the General Solution of \\(Sin \\theta\\) = 0 ?<\/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":[43,59],"tags":[],"yoast_head":"\nWhat is the General Solution of \\(Sin \\theta\\) = 0 ? - 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-general-solution-of-sin-theta-0\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the General Solution of \\(Sin \\theta\\) = 0 ? - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : The general solution of (sin theta) = 0 is given by (theta) = (npi), n (in) Z. 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