{"id":13839,"date":"2018-06-14T23:52:08","date_gmt":"2018-06-14T23:52:08","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/key-concepts-glossary-13\/"},"modified":"2018-06-14T23:52:08","modified_gmt":"2018-06-14T23:52:08","slug":"key-concepts-glossary-13","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/key-concepts-glossary-13\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"\n<section id=\"fs-id1165135186669\" class=\"key-equations\" data-depth=\"1\">\n<h2 data-type=\"title\">Key Equations<\/h2>\n<table id=\"eip-id1165137409421\" summary=\"..\">\n<tbody>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Cofunction Identities<\/td>\n<td>[latex]\\begin{array}{l}\\begin{array}{l}\\\\ \\cos t=\\sin \\left(\\frac{\\pi }{2}-t\\right)\\end{array}\\hfill \\\\ \\sin t=\\cos \\left(\\frac{\\pi }{2}-t\\right)\\hfill \\\\ \\tan t=\\cot \\left(\\frac{\\pi }{2}-t\\right)\\hfill \\\\ \\cot t=\\tan \\left(\\frac{\\pi }{2}-t\\right)\\hfill \\\\ \\sec t=\\csc \\left(\\frac{\\pi }{2}-t\\right)\\hfill \\\\ \\csc t=\\sec \\left(\\frac{\\pi }{2}-t\\right)\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section id=\"fs-id1165137481899\" class=\"key-concepts\" data-depth=\"1\">\n<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul id=\"fs-id1165137415357\">\n<li>We can define trigonometric functions as ratios of the side lengths of a right triangle.<\/li>\n<li>The same side lengths can be used to evaluate the trigonometric functions of either acute angle in a right triangle.<\/li>\n<li>We can evaluate the trigonometric functions of special angles, knowing the side lengths of the triangles in which they occur.<\/li>\n<li>Any two complementary angles could be the two acute angles of a right triangle.<\/li>\n<li>If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa.<\/li>\n<li>We can use trigonometric functions of an angle to find unknown side lengths.<\/li>\n<li>Select the trigonometric function representing the ratio of the unknown side to the known side.<\/li>\n<li>Right-triangle trigonometry permits the measurement of inaccessible heights and distances.<\/li>\n<li>The unknown height or distance can be found by creating a right triangle in which the unknown height or distance is one of the sides, and another side and angle are known.<\/li>\n<\/ul>\n<div data-type=\"glossary\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165137446119\" class=\"definition\">\n<dt>adjacent side<\/dt>\n<dd id=\"fs-id1165137446123\">in a right triangle, the side between a given angle and the right angle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137465232\" class=\"definition\">\n<dt>angle of depression<\/dt>\n<dd id=\"fs-id1165135175026\">the angle between the horizontal and the line from the object to the observer\u2019s eye, assuming the object is positioned lower than the observer<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137447602\" class=\"definition\">\n<dt>angle of elevation<\/dt>\n<dd id=\"fs-id1165135185281\">the angle between the horizontal and the line from the object to the observer\u2019s eye, assuming the object is positioned higher than the observer<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137558543\" class=\"definition\">\n<dt>opposite side<\/dt>\n<dd id=\"fs-id1165137558547\">in a right triangle, the side most distant from a given angle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135477488\" class=\"definition\">\n<dt>hypotenuse<\/dt>\n<dd id=\"fs-id1165137588091\">the side of a right triangle opposite the right angle<\/dd>\n<\/dl>\n<\/div>\n<p>&nbsp;<\/p>\n<\/section>\n\n","rendered":"<section id=\"fs-id1165135186669\" class=\"key-equations\" data-depth=\"1\">\n<h2 data-type=\"title\">Key Equations<\/h2>\n<table id=\"eip-id1165137409421\" summary=\"..\">\n<tbody>\n<tr>\n<td data-valign=\"top\" data-align=\"left\">Cofunction Identities<\/td>\n<td>[latex]\\begin{array}{l}\\begin{array}{l}\\\\ \\cos t=\\sin \\left(\\frac{\\pi }{2}-t\\right)\\end{array}\\hfill \\\\ \\sin t=\\cos \\left(\\frac{\\pi }{2}-t\\right)\\hfill \\\\ \\tan t=\\cot \\left(\\frac{\\pi }{2}-t\\right)\\hfill \\\\ \\cot t=\\tan \\left(\\frac{\\pi }{2}-t\\right)\\hfill \\\\ \\sec t=\\csc \\left(\\frac{\\pi }{2}-t\\right)\\hfill \\\\ \\csc t=\\sec \\left(\\frac{\\pi }{2}-t\\right)\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section id=\"fs-id1165137481899\" class=\"key-concepts\" data-depth=\"1\">\n<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul id=\"fs-id1165137415357\">\n<li>We can define trigonometric functions as ratios of the side lengths of a right triangle.<\/li>\n<li>The same side lengths can be used to evaluate the trigonometric functions of either acute angle in a right triangle.<\/li>\n<li>We can evaluate the trigonometric functions of special angles, knowing the side lengths of the triangles in which they occur.<\/li>\n<li>Any two complementary angles could be the two acute angles of a right triangle.<\/li>\n<li>If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa.<\/li>\n<li>We can use trigonometric functions of an angle to find unknown side lengths.<\/li>\n<li>Select the trigonometric function representing the ratio of the unknown side to the known side.<\/li>\n<li>Right-triangle trigonometry permits the measurement of inaccessible heights and distances.<\/li>\n<li>The unknown height or distance can be found by creating a right triangle in which the unknown height or distance is one of the sides, and another side and angle are known.<\/li>\n<\/ul>\n<div data-type=\"glossary\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165137446119\" class=\"definition\">\n<dt>adjacent side<\/dt>\n<dd id=\"fs-id1165137446123\">in a right triangle, the side between a given angle and the right angle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137465232\" class=\"definition\">\n<dt>angle of depression<\/dt>\n<dd id=\"fs-id1165135175026\">the angle between the horizontal and the line from the object to the observer\u2019s eye, assuming the object is positioned lower than the observer<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137447602\" class=\"definition\">\n<dt>angle of elevation<\/dt>\n<dd id=\"fs-id1165135185281\">the angle between the horizontal and the line from the object to the observer\u2019s eye, assuming the object is positioned higher than the observer<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137558543\" class=\"definition\">\n<dt>opposite side<\/dt>\n<dd id=\"fs-id1165137558547\">in a right triangle, the side most distant from a given angle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135477488\" class=\"definition\">\n<dt>hypotenuse<\/dt>\n<dd id=\"fs-id1165137588091\">the side of a right triangle opposite the right angle<\/dd>\n<\/dl>\n<\/div>\n<p>&nbsp;<\/p>\n<\/section>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-13839\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: OpenStax College. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":23485,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Precalculus\",\"author\":\"OpenStax College\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-13839","chapter","type-chapter","status-publish","hentry"],"part":13821,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/13839","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/users\/23485"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/13839\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/parts\/13821"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/13839\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/media?parent=13839"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapter-type?post=13839"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/contributor?post=13839"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/license?post=13839"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}