What fraction is tan 90?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The value of (\\tan(90^\\circ)) is undefined. This can be explained by understanding the definition of the tangent function and its behavior at this angle.<\/p>\n\n\n\n The tangent function in trigonometry is defined as the ratio of the opposite side to the adjacent side in a right triangle. More formally, for an angle (\\theta) in a right triangle, we have: At (\\theta = 90^\\circ), we know that:<\/p>\n\n\n\n Thus, the tangent of (90^\\circ) is: Since division by zero is undefined in mathematics, (\\tan(90^\\circ)) is undefined.<\/p>\n\n\n\n If you look at the graph of the tangent function, it is a periodic curve that repeats every (180^\\circ). The graph approaches infinity as it gets closer to (90^\\circ) from the left and negative infinity as it approaches from the right. There is a vertical asymptote at (90^\\circ), meaning the function does not have a finite value at this angle, confirming that (\\tan(90^\\circ)) is undefined.<\/p>\n\n\n\n In summary, (\\tan(90^\\circ)) is undefined because the cosine of (90^\\circ) is zero, and dividing by zero is not allowed in mathematics. Therefore, there is no numerical value for (\\tan(90^\\circ)), and it is considered to be undefined.<\/p>\n","protected":false},"excerpt":{"rendered":" What fraction is tan 90? The Correct Answer and Explanation is : The value of (\\tan(90^\\circ)) is undefined. This can be explained by understanding the definition of the tangent function and its behavior at this angle. Definition of Tangent: The tangent function in trigonometry is defined as the ratio of the opposite side to the […]<\/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-164653","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164653","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=164653"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164653\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=164653"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=164653"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=164653"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Definition of Tangent:<\/h3>\n\n\n\n
[
\\tan(\\theta) = \\frac{\\text{opposite}}{\\text{adjacent}}
]
Alternatively, in terms of sine and cosine, the tangent of an angle can be written as:
[
\\tan(\\theta) = \\frac{\\sin(\\theta)}{\\cos(\\theta)}
]
This formula tells us that the tangent is the ratio of the sine to the cosine of the angle.<\/p>\n\n\n\nBehavior at (90^\\circ):<\/h3>\n\n\n\n
\n
[
\\tan(90^\\circ) = \\frac{\\sin(90^\\circ)}{\\cos(90^\\circ)} = \\frac{1}{0}
]<\/p>\n\n\n\nGraphical Interpretation:<\/h3>\n\n\n\n
Conclusion:<\/h3>\n\n\n\n