{"id":8120,"date":"2014-12-11T19:06:14","date_gmt":"2014-12-11T19:06:14","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=8120"},"modified":"2014-12-11T19:06:14","modified_gmt":"2014-12-11T19:06:14","slug":"math-review-of-trigonometric-identities","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/12\/11\/math-review-of-trigonometric-identities\/","title":{"rendered":"Math Review of Trigonometric Identities"},"content":{"rendered":"

Overview<\/h3>\n

Trigonometric identities are relationships between trigonometric ratios that define them in terms of one another. They can be used to help solve problems that involve trigonometric functions.<\/p>\n

Reciprocal Identities<\/h3>\n

The reciprocal function to the sine is the cosecant, to the cosine is the secant, and to the tangent is the cotangent. In math language, the csc x = 1\/sin x; sec x = 1\/cos x, and cot x = 1\/tan x. If tan x =sin x\/cos x, then cot x also equals cos x\/sin x. The reciprocal identities are helpful because all trigonometric ratios in a problem can be rewritten in terms of sines and cosines, which are often much easier to use.<\/p>\n

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Pythagorean Identities<\/h3>\n

The Pythagorean identities are sin2<\/sup>x + cos2<\/sup>=1; tan2<\/sup>x +1 = sec2<\/sup>x; and 1 + cot2<\/sup>x = csc2<\/sup>x. Using the Pythagorean identities, one expression can be solved in terms of another by using substitution. The important thing to remember is that the\u00a0ratios are squared ratios, similar to using the Pythagorean Theorem with right triangles.<\/p>\n

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Using Known Information<\/h3>\n

One way to solve a trigonometric expression is to make sure that any rules of algebra are followed. For example, fractions can be put into common denominators and combined, using like denominators. Suppose that the fractions to be added are sin \u03b8\/cos \u03b8 +cos \u03b8\/ (1 + sin \u03b8). In order to add the fractions, they must have common denominators. Therefore, (sin \u03b8 [1 +sin \u03b8] +cos2<\/sup>\u03b8)\/ (cos \u03b8 (1 + sin \u03b8) can be simplified to 1\/cos \u03b8, which is sec \u03b8.<\/p>\n

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Simplifying Trigonometric Expressions<\/h3>\n

Another key to simplifying trigonometric expressions is to write them in terms of sines and cosines, because they are often easier to use. Tables are written with values of sines and cosines. Also, many of the common formulas, such as the area of a triangle, express values using the sine of an angle, and the Law of Sines and the Law of Cosines can be used to solve values for the triangle. Applications are much easier to use when the trigonometric expression is simplified.<\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Buffalo, NY: visit: Tutoring in Buffalo, NY<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview Trigonometric identities are relationships between trigonometric ratios that define them in terms of one another. They can be used to help solve problems that involve trigonometric functions. Reciprocal Identities The reciprocal function to the sine is the cosecant, to the cosine is the secant, and to the tangent is the cotangent. In math language, […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[14,18],"tags":[3594,3593,3592],"class_list":["post-8120","post","type-post","status-publish","format-standard","hentry","category-pre-calculus","category-trigonometry","tag-pythagorean-identities","tag-reciprocal-identities","tag-trigonometric-identities"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8120","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=8120"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8120\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=8120"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=8120"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=8120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}