{"id":12878,"date":"2015-10-29T18:32:44","date_gmt":"2015-10-29T18:32:44","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=12878"},"modified":"2015-10-29T18:32:44","modified_gmt":"2015-10-29T18:32:44","slug":"math-trigonometry-reference-angles","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-trigonometry-reference-angles\/","title":{"rendered":"Math:  trigonometry:  reference angles"},"content":{"rendered":"<h1>The tutor offers a couple of illustrations of an important concept from trigonometry.<\/h1>\n<p>When an angle is drawn in standard position, it opens counterclockwise from the positive x axis.<\/p>\n<p><strong>Example 1:  Show the angle 160\u00b0 in standard position, along with its reference angle.  Also label the quadrants.<\/strong><\/p>\n<p><img decoding=\"async\" src=\"\/..\/images\/refangle0.png\" style=\"display:block;margin:auto\"\/><\/p>\n<p>The reference angle is always thought to be positive and is always measured from the x axis to where the angle finishes.<\/p>\n<p><strong>Example 2:  Draw the angle in Quadrant III whose reference angle is 35\u00b0.<\/strong><\/p>\n<p><img decoding=\"async\" src=\"\/..\/images\/refangle1.png\" style=\"display:block;margin:auto\"\/><\/p>\n<p>We see that the QIII angle with reference 35\u00b0 has actual measure 215\u00b0.<\/p>\n<p>The QIV angle with reference 35\u00b0 is 325\u00b0.<\/p>\n<p>HTH:)<\/p>\n<p>Source:<\/p>\n<p>Travers, Kenneth J et al.  <u>Using Advanced Algebra.<\/u>  Toronto:  Doubleday Canada, 1977.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor offers a couple of illustrations of an important concept from trigonometry. When an angle is drawn in standard position, it opens counterclockwise from the positive x axis. Example 1: Show the angle 160\u00b0 in standard position, along with &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-trigonometry-reference-angles\/\"> <span class=\"screen-reader-text\">Math:  trigonometry:  reference angles<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[1155,1154,1152,1153],"class_list":["post-12878","post","type-post","status-publish","format-standard","hentry","category-math","tag-angle-in-standard-position","tag-reference-angle","tag-trig","tag-trigonometry"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/12878","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=12878"}],"version-history":[{"count":12,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/12878\/revisions"}],"predecessor-version":[{"id":12890,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/12878\/revisions\/12890"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=12878"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=12878"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=12878"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}