{"id":7844,"date":"2012-11-23T18:33:11","date_gmt":"2012-11-23T18:33:11","guid":{"rendered":"http:\/\/testpreparations.com\/help\/?p=2726"},"modified":"2014-12-02T08:31:56","modified_gmt":"2014-12-02T08:31:56","slug":"trigonometry-identity","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/11\/23\/trigonometry-identity\/","title":{"rendered":"Mathematics Review: Proving Trigonometry Identities"},"content":{"rendered":"

Trigonometry identity questions are usually you are given an equation and you have to change either left or right side in to another, using the properties below.<\/p>\n

 <\/p>\n

\n\n\n\n\n\n\n\n
sin \u03b8<\/td>\n\u00a0=<\/td>\n\u00a0\u00a0 1\u00a0\u00a0<\/span>
\ncsc \u03b8<\/td>\n		<\/td>\ncsc \u03b8<\/td>\n\u00a0=<\/td>\n\u00a0\u00a0 1\u00a0\u00a0<\/span>
\nsin \u03b8<\/td>\n<\/tr>\n
<\/td>\n<\/tr>\n
cos \u03b8<\/td>\n\u00a0=<\/td>\n\u00a0\u00a0 1\u00a0\u00a0<\/span>
\nsec \u03b8<\/td>\n		<\/td>\nsec \u03b8<\/td>\n\u00a0=<\/td>\n\u00a0\u00a0 1\u00a0\u00a0<\/span>
\ncos \u03b8<\/td>\n<\/tr>\n
<\/td>\n<\/tr>\n
tan \u03b8<\/td>\n\u00a0=<\/td>\n\u00a0\u00a0 1\u00a0\u00a0<\/span>
\ncot \u03b8<\/td>\n		<\/td>\ncot \u03b8<\/td>\n\u00a0=<\/td>\n\u00a0\u00a0 1\u00a0\u00a0<\/span>
\ntan \u03b8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

 <\/p>\n

 <\/p>\n

\n\n\n\n
tan \u03b8\u00a0 =<\/td>\nsin \u03b8<\/span>
\ncos \u03b8<\/td>\n		<\/td>\ncot \u03b8\u00a0 =<\/td>\ncos \u03b8<\/span>
\nsin \u03b8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

 <\/p>\n

\n\n\n\n\n
<\/td>\n\n

sin\u00b2\u03b8 + cos\u00b2\u03b8<\/p>\n<\/td>\n

\u00a0 =<\/td>\n1<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

 <\/p>\n

\n\n\n\n\n\n\n
\n

sin ( A+ \u03b2)<\/p>\n<\/td>\n

\u00a0 =<\/td>\nsin A cos \u03b2 + cos A sin \u03b2<\/td>\n<\/tr>\n
\n

sin ( A\u2212 \u03b2)<\/p>\n<\/td>\n

\u00a0 =<\/td>\nsin A cos \u03b2 \u2212 cos A sin \u03b2<\/td>\n<\/tr>\n
\n

cos ( A+ \u03b2)<\/p>\n<\/td>\n

\u00a0 =<\/td>\ncos A cos \u03b2 \u2212 sin A sin \u03b2<\/td>\n<\/tr>\n
\n

cos ( A\u2212 \u03b2)<\/p>\n<\/td>\n

\u00a0 =<\/td>\ncos A cos \u03b2 + sin A sin \u03b2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

 <\/p>\n

Most of the trig identity questions can be solved using these properties.<\/p>\n

To prove a trig identity, you need to change one of the sides. The tip to solve trig identities is to pick more complicated looking side, and change it into a simpler side.<\/p>\n

 <\/p>\n

First step of the transforming a trig identity is to change all of the terms in sine and cosine. As tangent, secant, cosecant, cotangent all of the terms can be changed into terms sine and cosine.<\/p>\n

 <\/p>\n

Second step is to use \u00a0property sin\u00b2\u03b8+ cos\u00b2\u03b8 =1 to simply the equations.<\/p>\n

 <\/p>\n

Third step is to arrange the terms into the other side.<\/p>\n

 <\/p>\n

Example:<\/p>\n

 <\/p>\n

sin\u00a0y<\/em>+sin\u00a0y<\/em>\u00a0cot^2<\/em>y<\/em>=csc\u00a0y<\/em><\/p>\n

\u00a0<\/em><\/p>\n

Pick left side since it is more complicated one.<\/p>\n

First step is to change cot into sine and cosine.<\/p>\n

Siny + siny(cosy\/siny)^2<\/p>\n

= Siny + cos^2y \/ siny<\/p>\n

= (sin^2y + cos^2y)\/ siny<\/p>\n

Since sin^2y + cos^2y = 1 apply this equation<\/p>\n

= 1\/siny<\/p>\n

 <\/p>\n

Now arrange this in terms of csc y<\/p>\n

1\/siny = csc y<\/p>\n

 <\/p>\n

Looking to get ready for the SAT? We can help with SAT Prep<\/a><\/p>\n

This article was written for you by Edmond<\/strong>, one of the tutors with Test Prep Academy.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Trigonometry identity questions are usually you are given an equation and you have to change either left or right side in to another, using the properties below.   sin \u03b8 \u00a0= \u00a0\u00a0 1\u00a0\u00a0 csc \u03b8 csc \u03b8 \u00a0= \u00a0\u00a0 1\u00a0\u00a0 sin \u03b8 cos \u03b8 \u00a0= \u00a0\u00a0 1\u00a0\u00a0 sec \u03b8 sec \u03b8 \u00a0= \u00a0\u00a0 1\u00a0\u00a0 cos […]<\/p>\n","protected":false},"author":6,"featured_media":3301,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2841,3015,3021,2851],"tags":[3126,3127,3321,3379,3397,3447],"class_list":["post-7844","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-act","category-math-act","category-mathematics-sat","category-sat","tag-how-do-you-use-trig","tag-how-do-you-use-trig-identities","tag-trigonometry-identity","tag-what-are-tirig-identities","tag-what-is-a-trigonometric-identity","tag-what-is-trig"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7844","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=7844"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7844\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media\/3301"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=7844"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=7844"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=7844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}