{“appState”:{“pageLoadApiCallsStatus”:true},”articleState”:{“article”:{“headers”:{“creationTime”:”2016-03-26T10:56:19+00:00″,”modifiedTime”:”2016-03-26T10:56:19+00:00″,”timestamp”:”2022-09-14T17:55:36+00:00″},”data”:{“breadcrumbs”:[{“name”:”Academics & The Arts”,”_links”:{“self”:”https://dummies-api.dummies.com/v2/categories/33662″},”slug”:”academics-the-arts”,”categoryId”:33662},{“name”:”Math”,”_links”:{“self”:”https://dummies-api.dummies.com/v2/categories/33720″},”slug”:”math”,”categoryId”:33720},{“name”:”Trigonometry”,”_links”:{“self”:”https://dummies-api.dummies.com/v2/categories/33729″},”slug”:”trigonometry”,”categoryId”:33729}],”title”:”Find the Trigonometry Function of an Angle in a Unit Circle”,”strippedTitle”:”find the trigonometry function of an angle in a unit circle”,”slug”:”find-the-trigonometry-function-of-an-angle-in-a-unit-circle”,”canonicalUrl”:””,”seo”:{“metaDescription”:”You can determine the trig functions for any angles found on the unit circle — any that are graphed in standard position (meaning the vertex of the angle is at “,”noIndex”:0,”noFollow”:0},”content”:”<p>You can determine the trig functions for any angles found on the unit circle — any that are graphed in <i>standard position</i> (meaning the vertex of the angle is at the origin, and the initial side lies along the positive <i>x-</i>axis). You use the rules for reference angles, the values of the functions of certain acute angles, and the rule for the signs of the functions.</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440368.image0.jpg\” width=\”535\” height=\”179\” alt=\”image0.jpg\”/>\n<img src=\”https://www.dummies.com/wp-content/uploads/440369.image1.jpg\” width=\”535\” height=\”354\” alt=\”image1.jpg\”/>\n<img src=\”https://www.dummies.com/wp-content/uploads/440370.image2.jpg\” width=\”389\” height=\”400\” alt=\”image2.jpg\”/>\n<p>Now, armed with all the necessary information, find the tangent of 300 degrees.</p>\n<ol class=\”level-one\”>\n <li><p class=\”first-para\”>Find the reference angle.</p>\n<p class=\”child-para\”>Using the top chart, you can see that a 300-degree angle has its terminal side in the fourth quadrant, so you find the reference angle by subtracting 300 from 360. Therefore, the measure of the reference angle is 60 degrees.</p>\n </li>\n <li><p class=\”first-para\”>Find the numerical value of the tangent.</p>\n<p class=\”child-para\”>Using the middle chart, you see that the numerical value of the tangent of 60 degrees is</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440371.image3.jpg\” width=\”31\” height=\”30\” alt=\”image3.jpg\”/>\n </li>\n <li><p class=\”first-para\”>Find the sign of the tangent.</p>\n<p class=\”child-para\”>Because a 300-degree angle is in the fourth quadrant, and angles in that quadrant have negative tangents (refer to the preceding section), the tangent of 300 degrees is</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440372.image4.jpg\” width=\”48\” height=\”30\” alt=\”image4.jpg\”/>\n </li>\n</ol>\n<p>To try your hand at working with radians, find the cosecant of</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440373.image5.jpg\” width=\”34\” height=\”57\” alt=\”image5.jpg\”/>\n<ol class=\”level-one\”>\n <li><p class=\”first-para\”>Find the reference angle.</p>\n<p class=\”child-para\”>To use the top chart, you need to determine the degree equivalence for an angle measuring</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440374.image6.jpg\” width=\”34\” height=\”57\” alt=\”image6.jpg\”/>\n<p class=\”child-para\”><b></b>Using the formula for converting from radians to degrees, you get that</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440375.image7.jpg\” width=\”34\” height=\”57\” alt=\”image7.jpg\”/>\n<p class=\”child-para\”>is equivalent to 210°. This angle is in the third quadrant, so, going back to radians, you find the reference angle by subtracting π from</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440376.image8.jpg\” width=\”34\” height=\”57\” alt=\”image8.jpg\”/>\n<p class=\”child-para\”>resulting in</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440377.image9.jpg\” width=\”125\” height=\”57\” alt=\”image9.jpg\”/>\n </li>\n <li><p class=\”first-para\”>Find the numerical value of the cosecant.</p>\n<p class=\”child-para\”>In the middle chart 2, the cosecant doesn’t appear. However, the reciprocal of the cosecant is sine. So find the value of the sine, and use its reciprocal. The sine of</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440378.image10.png\” width=\”58\” height=\”45\” alt=\”image10.png\”/>\n<p class=\”child-para\”><b></b>which means that the cosecant of</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440379.image11.jpg\” width=\”22\” height=\”57\” alt=\”image11.jpg\”/>\n<p class=\”child-para\”>is 2 (the reciprocal).</p>\n </li>\n <li><p class=\”first-para\”>Find the sign of the cosecant.</p>\n<p class=\”child-para\”>In the third quadrant, the cosecant of an angle is negative, so the cosecant of</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440380.image12.png\” width=\”80\” height=\”45\” alt=\”image12.png\”/>\n </li>\n</ol>”,”description”:”<p>You can determine the trig functions for any angles found on the unit circle — any that are graphed in <i>standard position</i> (meaning the vertex of the angle is at the origin, and the initial side lies along the positive <i>x-</i>axis). You use the rules for reference angles, the values of the functions of certain acute angles, and the rule for the signs of the functions.</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440368.image0.jpg\” width=\”535\” height=\”179\” alt=\”image0.jpg\”/>\n<img src=\”https://www.dummies.com/wp-content/uploads/440369.image1.jpg\” width=\”535\” height=\”354\” alt=\”image1.jpg\”/>\n<img src=\”https://www.dummies.com/wp-content/uploads/440370.image2.jpg\” width=\”389\” height=\”400\” alt=\”image2.jpg\”/>\n<p>Now, armed with all the necessary information, find the tangent of 300 degrees.</p>\n<ol class=\”level-one\”>\n <li><p class=\”first-para\”>Find the reference angle.</p>\n<p class=\”child-para\”>Using the top chart, you can see that a 300-degree angle has its terminal side in the fourth quadrant, so you find the reference angle by subtracting 300 from 360. Therefore, the measure of the reference angle is 60 degrees.</p>\n </li>\n <li><p class=\”first-para\”>Find the numerical value of the tangent.</p>\n<p class=\”child-para\”>Using the middle chart, you see that the numerical value of the tangent of 60 degrees is</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440371.image3.jpg\” width=\”31\” height=\”30\” alt=\”image3.jpg\”/>\n </li>\n <li><p class=\”first-para\”>Find the sign of the tangent.</p>\n<p class=\”child-para\”>Because a 300-degree angle is in the fourth quadrant, and angles in that quadrant have negative tangents (refer to the preceding section), the tangent of 300 degrees is</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440372.image4.jpg\” width=\”48\” height=\”30\” alt=\”image4.jpg\”/>\n </li>\n</ol>\n<p>To try your hand at working with radians, find the cosecant of</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440373.image5.jpg\” width=\”34\” height=\”57\” alt=\”image5.jpg\”/>\n<ol class=\”level-one\”>\n <li><p class=\”first-para\”>Find the reference angle.</p>\n<p class=\”child-para\”>To use the top chart, you need to determine the degree equivalence for an angle measuring</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440374.image6.jpg\” width=\”34\” height=\”57\” alt=\”image6.jpg\”/>\n<p class=\”child-para\”><b></b>Using the formula for converting from radians to degrees, you get that</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440375.image7.jpg\” width=\”34\” height=\”57\” alt=\”image7.jpg\”/>\n<p class=\”child-para\”>is equivalent to 210°. This angle is in the third quadrant, so, going back to radians, you find the reference angle by subtracting π from</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440376.image8.jpg\” width=\”34\” height=\”57\” alt=\”image8.jpg\”/>\n<p class=\”child-para\”>resulting in</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440377.image9.jpg\” width=\”125\” height=\”57\” alt=\”image9.jpg\”/>\n </li>\n <li><p class=\”first-para\”>Find the numerical value of the cosecant.</p>\n<p class=\”child-para\”>In the middle chart 2, the cosecant doesn’t appear. However, the reciprocal of the cosecant is sine. So find the value of the sine, and use its reciprocal. The sine of</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440378.image10.png\” width=\”58\” height=\”45\” alt=\”image10.png\”/>\n<p class=\”child-para\”><b></b>which means that the cosecant of</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440379.image11.jpg\” width=\”22\” height=\”57\” alt=\”image11.jpg\”/>\n<p class=\”child-para\”>is 2 (the reciprocal).</p>\n </li>\n <li><p class=\”first-para\”>Find the sign of the cosecant.</p>\n<p class=\”child-para\”>In the third quadrant, the cosecant of an angle is negative, so the cosecant of</p>\n<img src=\”https://www.dummies.com/wp-content/uploads/440380.image12.png\” width=\”80\” height=\”45\” alt=\”image12.png\”/>\n </li>\n</ol>”,”blurb”:””,”authors”:[{“authorId”:8985,”name”:”Mary Jane Sterling”,”slug”:”mary-jane-sterling”,”description”:” <p><b>Mary Jane Sterling</b> is the author of <i>Algebra I For Dummies, Algebra Workbook For Dummies,</i> and many other <i>For Dummies</i> books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics. “,”hasArticle”:false,”_links”:{“self”:”https://dummies-api.dummies.com/v2/authors/8985″}}],”primaryCategoryTaxonomy”:{“categoryId”:33729,”title”:”Trigonometry”,”slug”:”trigonometry”,”_links”:{“self”:”https://dummies-api.dummies.com/v2/categories/33729″}},”secondaryCategoryTaxonomy”:{“categoryId”:0,”title”:null,”slug”:null,”_links”:null},”tertiaryCategoryTaxonomy”:{“categoryId”:0,”title”:null,”slug”:null,”_links”:null},”trendingArticles”:null,”inThisArticle”:[],”relatedArticles”:{“fromBook”:[{“articleId”:207754,”title”:”Trigonometry For Dummies Cheat Sheet”,”slug”:”trigonometry-for-dummies-cheat-sheet”,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/207754″}},{“articleId”:203563,”title”:”How to Recognize Basic Trig Graphs”,”slug”:”how-to-recognize-basic-trig-graphs”,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/203563″}},{“articleId”:203561,”title”:”How to Create a Table of Trigonometry Functions”,”slug”:”how-to-create-a-table-of-trigonometry-functions”,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/203561″}},{“articleId”:186910,”title”:”Comparing Cosine and Sine Functions in a Graph”,”slug”:”comparing-cosine-and-sine-functions-in-a-graph”,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/186910″}},{“articleId”:157287,”title”:”Signs of Trigonometry Functions in Quadrants”,”slug”:”signs-of-trigonometry-functions-in-quadrants”,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/157287″}}],”fromCategory”:[{“articleId”:207754,”title”:”Trigonometry For Dummies Cheat Sheet”,”slug”:”trigonometry-for-dummies-cheat-sheet”,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/207754″}},{“articleId”:203563,”title”:”How to Recognize Basic Trig Graphs”,”slug”:”how-to-recognize-basic-trig-graphs”,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/203563″}},{“articleId”:203561,”title”:”How to Create a Table of Trigonometry Functions”,”slug”:”how-to-create-a-table-of-trigonometry-functions”,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/203561″}},{“articleId”:199411,”title”:”Defining the Radian in Trigonometry”,”slug”:”defining-the-radian-in-trigonometry”,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/199411″}},{“articleId”:187511,”title”:”How to Use the Double-Angle Identity for Sine”,”slug”:”how-to-use-the-double-angle-identity-for-sine”,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/187511″}}]},”hasRelatedBookFromSearch”:false,”relatedBook”:{“bookId”:282640,”slug”:”trigonometry-for-dummies-2nd-edition”,”isbn”:”9781118827413″,”categoryList”:[“academics-the-arts”,”math”,”trigonometry”],”amazon”:{“default”:”https://www.amazon.com/gp/product/1118827414/ref=as_li_tl?ie=UTF8&tag=wiley01-20″,”ca”:”https://www.amazon.ca/gp/product/1118827414/ref=as_li_tl?ie=UTF8&tag=wiley01-20″,”indigo_ca”:”http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1118827414-item.html&cjsku=978111945484″,”gb”:”https://www.amazon.co.uk/gp/product/1118827414/ref=as_li_tl?ie=UTF8&tag=wiley01-20″,”de”:”https://www.amazon.de/gp/product/1118827414/ref=as_li_tl?ie=UTF8&tag=wiley01-20″},”image”:{“src”:”https://www.dummies.com/wp-content/uploads/trigonometry-for-dummies-2nd-edition-cover-9781118827413-203×255.jpg”,”width”:203,”height”:255},”title”:”Trigonometry For Dummies”,”testBankPinActivationLink”:””,”bookOutOfPrint”:false,”authorsInfo”:”<p><b data-author-id=\”8985\”>Mary Jane Sterling</b> is the author of <i>Algebra I For Dummies</i> and many other <i>For Dummies</i> titles. She has been teaching mathematics at Bradley University in Peoria, Illinois, for more than 30 years and has loved working with future business executives, physical therapists, teachers, and many others.</p>”,”authors”:[{“authorId”:8985,”name”:”Mary Jane Sterling”,”slug”:”mary-jane-sterling”,”description”:” <p><b>Mary Jane Sterling</b> is the author of <i>Algebra I For Dummies, Algebra Workbook For Dummies,</i> and many other <i>For Dummies</i> books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics. “,”hasArticle”:false,”_links”:{“self”:”https://dummies-api.dummies.com/v2/authors/8985″}}],”_links”:{“self”:”https://dummies-api.dummies.com/v2/books/”}},”collections”:[],”articleAds”:{“footerAd”:”<div class=\”du-ad-region row\” id=\”article_page_adhesion_ad\”><div class=\”du-ad-unit col-md-12\” data-slot-id=\”article_page_adhesion_ad\” data-refreshed=\”false\” \r\n data-target = \”[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;trigonometry&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781118827413&quot;]}]\” id=\”du-slot-6322159826323\”></div></div>”,”rightAd”:”<div class=\”du-ad-region row\” id=\”article_page_right_ad\”><div class=\”du-ad-unit col-md-12\” data-slot-id=\”article_page_right_ad\” data-refreshed=\”false\” \r\n data-target = 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