{"id":233042,"date":"2025-06-12T13:34:18","date_gmt":"2025-06-12T13:34:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233042"},"modified":"2025-06-12T13:34:20","modified_gmt":"2025-06-12T13:34:20","slug":"find-exact-value-of-sin-pi-4-and-explain-how-you-got-the-answer","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/find-exact-value-of-sin-pi-4-and-explain-how-you-got-the-answer\/","title":{"rendered":"Find exact value of sin (pi\/4) and explain how you got the answer"},"content":{"rendered":"\n

Find exact value of sin (pi\/4) and explain how you got the answer<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The exact value of\u202fsin(\u03c0\/4)<\/strong>\u202fis:sin\u2061(\u03c04)=22\\sin\\left(\\frac{\\pi}{4}\\right) = \\frac{\\sqrt{2}}{2}sin(4\u03c0\u200b)=22\u200b\u200b<\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To find the exact value of sin\u2061(\u03c04)\\sin(\\frac{\\pi}{4})sin(4\u03c0\u200b), first understand what this expression means. The angle \u03c04\\frac{\\pi}{4}4\u03c0\u200b radians is equivalent to 45 degrees because:\u03c04\u00d7180\u2218\u03c0=45\u2218\\frac{\\pi}{4} \\times \\frac{180^\\circ}{\\pi} = 45^\\circ4\u03c0\u200b\u00d7\u03c0180\u2218\u200b=45\u2218<\/p>\n\n\n\n

So, the problem is asking for the sine of 45 degrees.<\/p>\n\n\n\n

The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. This can be remembered using the mnemonic SOH<\/strong> from SOHCAHTOA:
Sine = Opposite \/ Hypotenuse<\/strong><\/p>\n\n\n\n

To find the exact sine value of 45\u00b0, imagine or construct a 45\u00b0\u201345\u00b0\u201390\u00b0 triangle<\/strong>. This is a special type of right triangle where the two non-right angles are equal. Because the angles are equal, the legs of the triangle are also equal in length.<\/p>\n\n\n\n

Assume each leg of this triangle has a length of 1 unit. By the Pythagorean Theorem:Hypotenuse=12+12=2\\text{Hypotenuse} = \\sqrt{1^2 + 1^2} = \\sqrt{2}Hypotenuse=12+12\u200b=2\u200b<\/p>\n\n\n\n

Now, using the sine definition:sin\u2061(45\u2218)=OppositeHypotenuse=12\\sin(45^\\circ) = \\frac{\\text{Opposite}}{\\text{Hypotenuse}} = \\frac{1}{\\sqrt{2}}sin(45\u2218)=HypotenuseOpposite\u200b=2\u200b1\u200b<\/p>\n\n\n\n

This expression can be rationalized by multiplying the numerator and denominator by 2\\sqrt{2}2\u200b:12\u00d722=22\\frac{1}{\\sqrt{2}} \\times \\frac{\\sqrt{2}}{\\sqrt{2}} = \\frac{\\sqrt{2}}{2}2\u200b1\u200b\u00d72\u200b2\u200b\u200b=22\u200b\u200b<\/p>\n\n\n\n

Therefore,sin\u2061(\u03c04)=22\\sin\\left(\\frac{\\pi}{4}\\right) = \\frac{\\sqrt{2}}{2}sin(4\u03c0\u200b)=22\u200b\u200b<\/p>\n\n\n\n

This is an exact<\/strong> value, commonly memorized as one of the standard trigonometric values on the unit circle.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Find exact value of sin (pi\/4) and explain how you got the answer The Correct Answer and Explanation is: The exact value of\u202fsin(\u03c0\/4)\u202fis:sin\u2061(\u03c04)=22\\sin\\left(\\frac{\\pi}{4}\\right) = \\frac{\\sqrt{2}}{2}sin(4\u03c0\u200b)=22\u200b\u200b Explanation: To find the exact value of sin\u2061(\u03c04)\\sin(\\frac{\\pi}{4})sin(4\u03c0\u200b), first understand what this expression means. The angle \u03c04\\frac{\\pi}{4}4\u03c0\u200b radians is equivalent to 45 degrees because:\u03c04\u00d7180\u2218\u03c0=45\u2218\\frac{\\pi}{4} \\times \\frac{180^\\circ}{\\pi} = 45^\\circ4\u03c0\u200b\u00d7\u03c0180\u2218\u200b=45\u2218 So, 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-233042","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233042","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=233042"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233042\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233042"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233042"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}