{"id":6062,"date":"2021-10-04T23:56:05","date_gmt":"2021-10-04T18:26:05","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6062"},"modified":"2021-10-04T23:56:24","modified_gmt":"2021-10-04T18:26:24","slug":"trigonometric-equation-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/trigonometric-equation-examples\/","title":{"rendered":"Trigonometric Equation Examples"},"content":{"rendered":"

Here you will learn some trigonometric equation examples for better understanding of trigonometric equation concepts<\/a><\/span>.<\/p>\n\n\n

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\n\n \n

Example 1 : <\/span>Find general solution of (2sinx – cosx)(1 + cosx) = \\(sin^2x\\)<\/p>\n

Solution : <\/span>(2sinx – cosx)(1 + cosx) – (1 – \\(cos^2x\\)) = 0

\n \\(\\therefore\\)   (1 + cosx)(2sinx – cosx – 1 + cosx) = 0

\n \\(\\therefore\\)   (1 + cosx)(2sinx – 1) = 0

\n \\(\\implies\\)   cosx = -1   or   sinx = \\(1\\over 2\\)

\n \\(\\implies\\)   cosx = -1 = cos\\(\\pi\\)   \\(\\implies\\)   x = 2n\\(\\pi\\) + \\(\\pi\\) = (2n+1)\\(\\pi\\), n \\(\\in\\) I\n

\n or   sinx = \\(1\\over 2\\) = sin\\(\\pi\\over 6\\)   \\(\\implies\\)   x = k\\(\\pi + (-1)^k{\\pi\\over 6}\\), k \\(\\in\\) I<\/p>\n


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Example 2 : <\/span> Solve : 6 – 10cosx = 3\\(sin^2x\\)<\/p>\n

Solution : <\/span>we have, 6 – 10cosx = 3\\(sin^2x\\)

\n \\(\\therefore\\)   6 – 10cosx = 3 – 3\\(cos^2x\\)

\n \\(\\implies\\)   3\\(cos^2x\\) – 10cosx + 3 = 0

\n \\(\\implies\\)   (3cosx-1)(cosx-3) = 0   \\(\\implies\\)   cosx = \\(1\\over 3\\) or cosx = 3

\n Since cosx =3 is not possible as -1 \\(\\le\\) cosx \\(\\le\\) 1

\n \\(\\therefore\\)   cosx = \\(1\\over 3\\) = cos(\\(cos^{-1}{1\\over 3}\\))   \\(\\implies\\)   x = 2n\\(\\pi\\) \\(\\pm\\) \\(cos^{-1}{1\\over 3}\\)<\/p>\n


\n\n \n

Example 3 : <\/span>Solve : cos3x + sin2x – sin4x = 0<\/p>\n

Solution : <\/span>we have, cos3x + (sin2x – sin4x) = 0

\n = cos3x – 2sinx.cos3x = 0

\n \\(\\implies\\)   (cos3x)(1 – 2sinx) = 0

\n \\(\\implies\\)   cos3x = 0   or   sinx = \\(1\\over 2\\)

\n \\(\\implies\\)   cos3x = 0 = cos\\(\\pi\\over 2\\)   or   sinx = \\(1\\over 2\\) = sin\\(\\pi\\over 6\\)

\n \\(\\implies\\)   3x = 2n\\(\\pi\\) \\(\\pm\\) \\(\\pi\\over 2\\)   or   x = m\\(\\pi\\) + \\({(-1)}^m\\)\\(\\pi\\over 6\\)

\n \\(\\implies\\)   x = \\(2n\\pi\\over 3\\) \\(\\pm\\) \\(\\pi\\over 6\\)   or   x = m\\(\\pi\\) + \\({(-1)}^m\\)\\(\\pi\\over 6\\); (n, m \\(\\in\\) I)\n <\/p>\n
\n

Practice these given trigonometric equation examples to test your knowledge on concepts of trigonometric equation.<\/p>\n \n <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn some trigonometric equation examples for better understanding of trigonometric equation concepts. Example 1 : Find general solution of (2sinx – cosx)(1 + cosx) = \\(sin^2x\\) Solution : (2sinx – cosx)(1 + cosx) – (1 – \\(cos^2x\\)) = 0 \\(\\therefore\\)   (1 + cosx)(2sinx – cosx – 1 + cosx) = 0 …<\/p>\n

Trigonometric Equation Examples<\/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":[29],"tags":[],"yoast_head":"\nTrigonometric Equation Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"Solve these Trigonometric Equation examples to practice and test your knowledge of Trigonometric Equation concepts.\" \/>\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\/trigonometric-equation-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Trigonometric Equation Examples - 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