To further justify the Cofunction Theorem, use your calculator to find a value for the pair of trigonometric functions below. In this case, the trigonometric functions are cofunctions of one another, and the angles are complementary angles. Round each answer to four decimal places.<\/p>\n\n\n\n
sin28deg
, ?cos62deg<\/p>\n\n\n\n
sin(28\\deg ) = ?<\/p>\n\n\n\n
cos(62\\deg )<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n o illustrate the Cofunction Theorem, let’s calculate the values of sin(28\u00b0) and cos(62\u00b0) using a calculator, rounding each to four decimal places: \ue200video\ue202The Cofunction Theorem\ue202turn0search7\ue201<\/p>\n","protected":false},"excerpt":{"rendered":" To further justify the Cofunction Theorem, use your calculator to find a value for the pair of trigonometric functions below. In this case, the trigonometric functions are cofunctions of one another, and the angles are complementary angles. Round each answer to four decimal places. sin28deg, ?cos62deg sin(28\\deg ) = ? cos(62\\deg ) The Correct Answer […]<\/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-187655","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187655","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=187655"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187655\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187655"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187655"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187655"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
in(28\u00b0) \u2248 0.4695
os(62\u00b0) \u2248 0.4695
hese results are equal, which exemplifies the Cofunction Theorem.
he Cofunction Theorem states that the value of a trigonometric function of an angle is equal to the value of its cofunction at the complementary angle.n mathematical terms, for an angle \u03b8:
in(\u03b8) = cos(90\u00b0 \u2212 \u03b8)
os(\u03b8) = sin(90\u00b0 \u2212 \u03b8)
an(\u03b8) = cot(90\u00b0 \u2212 \u03b8)
ot(\u03b8) = tan(90\u00b0 \u2212 \u03b8)
ec(\u03b8) = csc(90\u00b0 \u2212 \u03b8)
sc(\u03b8) = sec(90\u00b0 \u2212 \u03b8)
n our example, \u03b8 is 28\u00b0, making its complementary angle 62\u00b0 (since 90\u00b0 \u2212 28\u00b0 = 62\u00b0).ccording to the Cofunction Theorem:
in(28\u00b0) = cos(62\u00b0)
his relationship arises from the definitions of sine and cosine in a right-angled triangle.he sine of an angle is the ratio of the length of the side opposite the angle to the hypotenuse, while the cosine of an angle is the ratio of the length of the adjacent side to the hypotenuse.or two complementary angles in a right-angled triangle, the side opposite one angle is the side adjacent to the other, leading to these cofunction identities.
nderstanding the Cofunction Theorem is crucial in trigonometry as it highlights the inherent relationships between trigonometric functions and their complementary angles.his knowledge simplifies the analysis of trigonometric expressions and aids in solving equations involving complementary angles.
For a more in-depth explanation, you might find this video helpful:<\/p>\n\n\n\n