{"id":13754,"date":"2018-06-14T23:49:18","date_gmt":"2018-06-14T23:49:18","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/key-concepts-glossary-3\/"},"modified":"2018-06-14T23:49:18","modified_gmt":"2018-06-14T23:49:18","slug":"key-concepts-glossary-3","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/key-concepts-glossary-3\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"\n<section id=\"fs-id1165135369540\" class=\"key-equations\" data-depth=\"1\">\n<h2 data-type=\"title\">Key Equations<\/h2>\n<table id=\"eip-id1165134342478\" summary=\"..\">\n<tbody>\n<tr>\n<td>arc length<\/td>\n<td>[latex]s=r\\theta [\/latex]<\/td>\n<\/tr>\n<tr>\n<td>area of a sector<\/td>\n<td>[latex]A=\\frac{1}{2}\\theta {r}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>angular speed<\/td>\n<td>[latex]\\omega =\\frac{\\theta }{t}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>linear speed<\/td>\n<td>[latex]v=\\frac{s}{t}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>linear speed related to angular speed<\/td>\n<td>[latex]v=r\\omega [\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section id=\"fs-id1165135431038\" class=\"key-concepts\" data-depth=\"1\">\n<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul id=\"fs-id1165135431044\">\n<li>An angle is formed from the union of two rays, by keeping the initial side fixed and rotating the terminal side. The amount of rotation determines the measure of the angle.<\/li>\n<li>An angle is in standard position if its vertex is at the origin and its initial side lies along the positive <em data-effect=\"italics\">x<\/em>-axis. A positive angle is measured counterclockwise from the initial side and a negative angle is measured clockwise.<\/li>\n<li>To draw an angle in standard position, draw the initial side along the positive <em data-effect=\"italics\">x<\/em>-axis and then place the terminal side according to the fraction of a full rotation the angle represents.<\/li>\n<li>In addition to degrees, the measure of an angle can be described in radians.<\/li>\n<li>To convert between degrees and radians, use the proportion [latex]\\frac{\\theta }{180}=\\frac{{\\theta }^{R}}{\\pi }[\/latex].<\/li>\n<li>Two angles that have the same terminal side are called coterminal angles.<\/li>\n<li>We can find coterminal angles by adding or subtracting 360\u00b0 or [latex]2\\pi [\/latex].<\/li>\n<li>Coterminal angles can be found using radians just as they are for degrees.<\/li>\n<li>The length of a circular arc is a fraction of the circumference of the entire circle.<\/li>\n<li>The area of sector is a fraction of the area of the entire circle.<\/li>\n<li>An object moving in a circular path has both linear and angular speed.<\/li>\n<li>The angular speed of an object traveling in a circular path is the measure of the angle through which it turns in a unit of time.<\/li>\n<li>The linear speed of an object traveling along a circular path is the distance it travels in a unit of time.<\/li>\n<\/ul>\n<div data-type=\"glossary\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165135487231\" class=\"definition\">\n<dt>angle<\/dt>\n<dd id=\"fs-id1165135487236\">the union of two rays having a common endpoint<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135487241\" class=\"definition\">\n<dt>angular speed<\/dt>\n<dd id=\"fs-id1165135487246\">the angle through which a rotating object travels in a unit of time<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135487250\" class=\"definition\">\n<dt>arc length<\/dt>\n<dd id=\"fs-id1165135170996\">the length of the curve formed by an arc<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135171000\" class=\"definition\">\n<dt>area of a sector<\/dt>\n<dd id=\"fs-id1165135171006\">area of a portion of a circle bordered by two radii and the intercepted arc; the fraction [latex]\\frac{\\theta }{2\\pi }[\/latex] multiplied by the area of the entire circle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134223298\" class=\"definition\">\n<dt>coterminal angles<\/dt>\n<dd id=\"fs-id1165134223303\">description of positive and negative angles in standard position sharing the same terminal side<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134223307\" class=\"definition\">\n<dt>degree<\/dt>\n<dd id=\"fs-id1165134084943\">a unit of measure describing the size of an angle as one-360th of a full revolution of a circle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134084947\" class=\"definition\">\n<dt>initial side<\/dt>\n<dd id=\"fs-id1165134084952\">the side of an angle from which rotation begins<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134084957\" class=\"definition\">\n<dt>linear speed<\/dt>\n<dd id=\"fs-id1165134084962\">the distance along a straight path a rotating object travels in a unit of time; determined by the arc length<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135580273\" class=\"definition\">\n<dt>measure of an angle<\/dt>\n<dd id=\"fs-id1165135580278\">the amount of rotation from the initial side to the terminal side<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135580283\" class=\"definition\">\n<dt>negative angle<\/dt>\n<dd id=\"fs-id1165135580288\">description of an angle measured clockwise from the positive <em data-effect=\"italics\">x<\/em>-axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135580297\" class=\"definition\">\n<dt>positive angle<\/dt>\n<dd id=\"fs-id1165135519264\">description of an angle measured counterclockwise from the positive <em data-effect=\"italics\">x<\/em>-axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135519274\" class=\"definition\">\n<dt>quadrantal angle<\/dt>\n<dd id=\"fs-id1165135519280\">an angle whose terminal side lies on an axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135519284\" class=\"definition\">\n<dt>radian measure<\/dt>\n<dd id=\"fs-id1165135519289\">the ratio of the arc length formed by an angle divided by the radius of the circle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135193270\" class=\"definition\">\n<dt>radian<\/dt>\n<dd id=\"fs-id1165135193275\">the measure of a central angle of a circle that intercepts an arc equal in length to the radius of that circle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135193281\" class=\"definition\">\n<dt>ray<\/dt>\n<dd id=\"fs-id1165135193286\">one point on a line and all points extending in one direction from that point; one side of an angle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135193291\" class=\"definition\">\n<dt>reference angle<\/dt>\n<dd id=\"fs-id1165134298995\">the measure of the acute angle formed by the terminal side of the angle and the horizontal axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134299000\" class=\"definition\">\n<dt>standard position<\/dt>\n<dd id=\"fs-id1165134299005\">the position of an angle having the vertex at the origin and the initial side along the positive <em data-effect=\"italics\">x<\/em>-axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134299015\" class=\"definition\">\n<dt>terminal side<\/dt>\n<dd id=\"fs-id1165134299020\">the side of an angle at which rotation ends<\/dd>\n<\/dl>\n<dl id=\"fs-id1165133309879\" class=\"definition\">\n<dt>vertex<\/dt>\n<dd id=\"fs-id1165133309884\">the common endpoint of two rays that form an angle<\/dd>\n<\/dl>\n<\/div>\n<p>&nbsp;<\/p>\n<\/section>\n\n","rendered":"<section id=\"fs-id1165135369540\" class=\"key-equations\" data-depth=\"1\">\n<h2 data-type=\"title\">Key Equations<\/h2>\n<table id=\"eip-id1165134342478\" summary=\"..\">\n<tbody>\n<tr>\n<td>arc length<\/td>\n<td>[latex]s=r\\theta[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>area of a sector<\/td>\n<td>[latex]A=\\frac{1}{2}\\theta {r}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>angular speed<\/td>\n<td>[latex]\\omega =\\frac{\\theta }{t}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>linear speed<\/td>\n<td>[latex]v=\\frac{s}{t}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>linear speed related to angular speed<\/td>\n<td>[latex]v=r\\omega[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section id=\"fs-id1165135431038\" class=\"key-concepts\" data-depth=\"1\">\n<h2 data-type=\"title\">Key Concepts<\/h2>\n<ul id=\"fs-id1165135431044\">\n<li>An angle is formed from the union of two rays, by keeping the initial side fixed and rotating the terminal side. The amount of rotation determines the measure of the angle.<\/li>\n<li>An angle is in standard position if its vertex is at the origin and its initial side lies along the positive <em data-effect=\"italics\">x<\/em>-axis. A positive angle is measured counterclockwise from the initial side and a negative angle is measured clockwise.<\/li>\n<li>To draw an angle in standard position, draw the initial side along the positive <em data-effect=\"italics\">x<\/em>-axis and then place the terminal side according to the fraction of a full rotation the angle represents.<\/li>\n<li>In addition to degrees, the measure of an angle can be described in radians.<\/li>\n<li>To convert between degrees and radians, use the proportion [latex]\\frac{\\theta }{180}=\\frac{{\\theta }^{R}}{\\pi }[\/latex].<\/li>\n<li>Two angles that have the same terminal side are called coterminal angles.<\/li>\n<li>We can find coterminal angles by adding or subtracting 360\u00b0 or [latex]2\\pi[\/latex].<\/li>\n<li>Coterminal angles can be found using radians just as they are for degrees.<\/li>\n<li>The length of a circular arc is a fraction of the circumference of the entire circle.<\/li>\n<li>The area of sector is a fraction of the area of the entire circle.<\/li>\n<li>An object moving in a circular path has both linear and angular speed.<\/li>\n<li>The angular speed of an object traveling in a circular path is the measure of the angle through which it turns in a unit of time.<\/li>\n<li>The linear speed of an object traveling along a circular path is the distance it travels in a unit of time.<\/li>\n<\/ul>\n<div data-type=\"glossary\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1165135487231\" class=\"definition\">\n<dt>angle<\/dt>\n<dd id=\"fs-id1165135487236\">the union of two rays having a common endpoint<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135487241\" class=\"definition\">\n<dt>angular speed<\/dt>\n<dd id=\"fs-id1165135487246\">the angle through which a rotating object travels in a unit of time<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135487250\" class=\"definition\">\n<dt>arc length<\/dt>\n<dd id=\"fs-id1165135170996\">the length of the curve formed by an arc<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135171000\" class=\"definition\">\n<dt>area of a sector<\/dt>\n<dd id=\"fs-id1165135171006\">area of a portion of a circle bordered by two radii and the intercepted arc; the fraction [latex]\\frac{\\theta }{2\\pi }[\/latex] multiplied by the area of the entire circle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134223298\" class=\"definition\">\n<dt>coterminal angles<\/dt>\n<dd id=\"fs-id1165134223303\">description of positive and negative angles in standard position sharing the same terminal side<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134223307\" class=\"definition\">\n<dt>degree<\/dt>\n<dd id=\"fs-id1165134084943\">a unit of measure describing the size of an angle as one-360th of a full revolution of a circle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134084947\" class=\"definition\">\n<dt>initial side<\/dt>\n<dd id=\"fs-id1165134084952\">the side of an angle from which rotation begins<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134084957\" class=\"definition\">\n<dt>linear speed<\/dt>\n<dd id=\"fs-id1165134084962\">the distance along a straight path a rotating object travels in a unit of time; determined by the arc length<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135580273\" class=\"definition\">\n<dt>measure of an angle<\/dt>\n<dd id=\"fs-id1165135580278\">the amount of rotation from the initial side to the terminal side<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135580283\" class=\"definition\">\n<dt>negative angle<\/dt>\n<dd id=\"fs-id1165135580288\">description of an angle measured clockwise from the positive <em data-effect=\"italics\">x<\/em>-axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135580297\" class=\"definition\">\n<dt>positive angle<\/dt>\n<dd id=\"fs-id1165135519264\">description of an angle measured counterclockwise from the positive <em data-effect=\"italics\">x<\/em>-axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135519274\" class=\"definition\">\n<dt>quadrantal angle<\/dt>\n<dd id=\"fs-id1165135519280\">an angle whose terminal side lies on an axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135519284\" class=\"definition\">\n<dt>radian measure<\/dt>\n<dd id=\"fs-id1165135519289\">the ratio of the arc length formed by an angle divided by the radius of the circle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135193270\" class=\"definition\">\n<dt>radian<\/dt>\n<dd id=\"fs-id1165135193275\">the measure of a central angle of a circle that intercepts an arc equal in length to the radius of that circle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135193281\" class=\"definition\">\n<dt>ray<\/dt>\n<dd id=\"fs-id1165135193286\">one point on a line and all points extending in one direction from that point; one side of an angle<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135193291\" class=\"definition\">\n<dt>reference angle<\/dt>\n<dd id=\"fs-id1165134298995\">the measure of the acute angle formed by the terminal side of the angle and the horizontal axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134299000\" class=\"definition\">\n<dt>standard position<\/dt>\n<dd id=\"fs-id1165134299005\">the position of an angle having the vertex at the origin and the initial side along the positive <em data-effect=\"italics\">x<\/em>-axis<\/dd>\n<\/dl>\n<dl id=\"fs-id1165134299015\" class=\"definition\">\n<dt>terminal side<\/dt>\n<dd id=\"fs-id1165134299020\">the side of an angle at which rotation ends<\/dd>\n<\/dl>\n<dl id=\"fs-id1165133309879\" class=\"definition\">\n<dt>vertex<\/dt>\n<dd id=\"fs-id1165133309884\">the common endpoint of two rays that form an 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-13754\">\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":6,"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-13754","chapter","type-chapter","status-publish","hentry"],"part":13723,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/13754","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\/13754\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/parts\/13723"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapters\/13754\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/media?parent=13754"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/pressbooks\/v2\/chapter-type?post=13754"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/contributor?post=13754"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/wp-json\/wp\/v2\/license?post=13754"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}