The function y=sin\u2061(x)y = \\sin(x)y=sin(x) is one of the most fundamental trigonometric functions. It is defined for all real numbers, meaning its domain is the entire set of real numbers, R\\mathbb{R}R. The sine function does not have any restrictions on the input values of xxx, so we can say that the domain of y=sin\u2061(x)y = \\sin(x)y=sin(x) is:Domain:(\u2212\u221e,\u221e)\\text{Domain:} \\quad (-\\infty, \\infty)Domain:(\u2212\u221e,\u221e)<\/p>\n\n\n\n
Explanation of Domain<\/h3>\n\n\n\n
The sine function is periodic, and it repeats its values in a regular cycle as xxx increases or decreases. This periodicity means that no matter how large or small xxx becomes, the sine function will always produce a valid output. The sine function is defined for every real number, so there are no limitations on the values of xxx.<\/p>\n\n\n\n
Range of y=sin\u2061(x)y = \\sin(x)y=sin(x)<\/h3>\n\n\n\n
The sine function only takes values between -1 and 1, inclusive. This means that for every input xxx, the output y=sin\u2061(x)y = \\sin(x)y=sin(x) will always lie within the interval [\u22121,1][-1, 1][\u22121,1]. Mathematically, we express this as:Range:[\u22121,1]\\text{Range:} \\quad [-1, 1]Range:[\u22121,1]<\/p>\n\n\n\n
Explanation of Range<\/h3>\n\n\n\n
The sine function oscillates between -1 and 1 as xxx changes. The maximum value of sin\u2061(x)\\sin(x)sin(x) is 1, which occurs at x=\u03c02+2k\u03c0x = \\frac{\\pi}{2} + 2k\\pix=2\u03c0\u200b+2k\u03c0 for any integer kkk. The minimum value of sin\u2061(x)\\sin(x)sin(x) is -1, which occurs at x=3\u03c02+2k\u03c0x = \\frac{3\\pi}{2} + 2k\\pix=23\u03c0\u200b+2k\u03c0 for any integer kkk. This means that no matter the value of xxx, the sine of that number will never exceed 1 or go below -1.<\/p>\n\n\n\n
Thus, the domain of y=sin\u2061(x)y = \\sin(x)y=sin(x) is all real numbers, and the range is the closed interval from -1 to 1.<\/p>\n\n\n\n What are the domain and the range of y = sin x? The Correct Answer and Explanation is: The function y=sin\u2061(x)y = \\sin(x)y=sin(x) is one of the most fundamental trigonometric functions. It is defined for all real numbers, meaning its domain is the entire set of real numbers, R\\mathbb{R}R. The sine function does not have […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"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":"","ast-disable-related-posts":"","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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-241979","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241979","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=241979"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/241979\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=241979"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=241979"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=241979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-199.jpeg\")
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