{"id":71447,"date":"2021-04-12T11:41:06","date_gmt":"2021-04-12T16:41:06","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=71447"},"modified":"2026-03-28T12:21:52","modified_gmt":"2026-03-28T17:21:52","slug":"degrees-and-radians","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/degrees-and-radians\/","title":{"rendered":"Degrees and Radians Overview"},"content":{"rendered":"<h2 class=\"pt-page\" style=\"margin-top: 1em;\"><span id=\"What_are_Angles\" class=\"m-toc-anchor\"><\/span>What are Angles?<\/h2>\n<p>We use degrees as units of measurement for angles, and precisely determining how wide or narrow they are. The small circle symbol \u201c\u00b0&#8221; is used following a number to denote that degrees are being represented. Note the following classifications:<\/p>\n<ul>\n<li>An <strong>acute angle<\/strong> is between 0-90\u00b0<\/li>\n<li>A <strong>right angle<\/strong> is 90\u00b0<\/li>\n<li>An <strong>obtuse angle<\/strong> is between 90-180\u00b0<\/li>\n<li>A <strong>straight angle<\/strong> is 180\u00b0<\/li>\n<li>A <strong>reflex angle<\/strong> is between 180-360\u00b0<\/li>\n<li>A full circle contains 360\u00b0, and a 360\u00b0 angle is called a <strong>complete angle<\/strong><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-71477\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/diagram-of-the-different-types-of-angles-e1618243982151.png\" alt=\"diagram of the different types of angles\" width=\"399\" height=\"316\" \/><\/p>\n<p>Note that when we use angles on the Cartesian plane, the angles always begin on the positive \\(x\\)-axis and open in the counterclockwise direction. For this reason, the positive \\(x\\)-axis is referred to as 0\u00b0 in polar coordinates, which we will address later.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-71474\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Graph-of-a-particular-angle-with-one-side-along-the-x-axis.png\" alt=\"Graph of a particular angle with one side along the x axis\" width=\"318.3\" height=\"311.7\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Graph-of-a-particular-angle-with-one-side-along-the-x-axis.png 1061w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Graph-of-a-particular-angle-with-one-side-along-the-x-axis-300x294.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Graph-of-a-particular-angle-with-one-side-along-the-x-axis-1024x1003.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Graph-of-a-particular-angle-with-one-side-along-the-x-axis-768x752.png 768w\" sizes=\"(max-width: 1061px) 100vw, 1061px\" \/><\/p>\n<p>Radians are simply another way of measuring angles. Rather than divide a circle into 360 tiny \u201cslices,\u201d radians offer a clever and intuitive way to measure angles. One radian is the angle at which the radius of the circle equals the length of the arc of the curve drawn with that angle.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-71471\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/diagram-of-a-radian-e1618244072548.png\" alt=\"diagram of a radian\" width=\"403.55\" height=\"338.1\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/diagram-of-a-radian-e1618244072548.png 1153w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/diagram-of-a-radian-e1618244072548-300x251.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/diagram-of-a-radian-e1618244072548-1024x858.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/diagram-of-a-radian-e1618244072548-768x643.png 768w\" sizes=\"(max-width: 1153px) 100vw, 1153px\" \/><\/p>\n<p>Notice from the illustration above that the angle of one radian is almost one sixth of the circle. So how many radians are in a full revolution then? Recall the relationship between the radius of a circle and its circumference.<\/p>\n<p style=\"text-align: center;\">\\(C = 2r\\)<\/p>\n<p>The circumference of a circle is equal to \\(\\pi\\) times its diameter, or equivalently, times twice its radius. And since the length of the circle\u2019s radius is equal to one radian, the circumference is equal to \\(2\\pi\\) radians. In other words, one full revolution contains \\(2\\pi\\) radians.<\/p>\n<p>We most commonly use radians when dealing with the trigonometric functions (sin, cos, tan, csc, sec, and cot).<\/p>\n<div class=\"buttonlinks\"><a href=\"#pqs\">Degrees and Radians Sample Questions<\/a><\/div>\n<h2 class=\"pt-page\"><span id=\"Degrees_to_Radians\" class=\"m-toc-anchor\"><\/span>Degrees to Radians<\/h2>\n<p>How do we convert from degrees to radians? We need a way to convert our number of degrees into some number of radians, so we will derive a conversion factor with which to do so. Remember that there are 360\u00b0 in a circle, and that there are \\(2\\pi\\) radians in a circle. This means that \\(360\\text{ degrees}=2\\pi\\text{ radians}\\).<\/p>\n<p>We can divide both sides by 2 to simplify this equation to \\(180\\text{ degrees}=\\pi\\text{ radians}\\).<\/p>\n<p>Finally, we are going to divide both sides by 180 degrees.<\/p>\n<p style=\"text-align: center;\">\\(\\frac{180\\text{ degrees}}{180\\text{ degrees}}=\\frac{\u03c0\\text{ radians}}{180\\text{ degrees}}\\)<\/p>\n<p style=\"text-align: center;\">\\(1=\\frac{\u03c0\\text{ radians}}{180\\text{ degrees}}\\)<\/p>\n<p>What exactly have we ended up with here? Because \\(\\frac{\u03c0\\text{ radians}}{180\\text{ degrees}}\\) is equal to 1, we can multiply our number of degrees by this conversion factor without changing their value. The \u201cdegrees\u201d units will cancel with each other, leaving us with radians once we simplify the numerical values!<\/p>\n<p style=\"text-align: center;\"><strong>Our constant for converting degrees to radians is<\/strong>\\(\\mathbf{\\frac{\u03c0\\text{ radians}}{180\\text{ degrees}}}\\)<\/p>\n<h3><span id=\"Conversion_Example\" class=\"m-toc-anchor\"><\/span>Conversion Example<\/h3>\n<p>Let\u2019s work an example by converting 120\u00b0 to radians. To begin, we multiply 120 degrees by our conversion factor, \\(\\frac{\u03c0\\text{ radians}}{180\\text{ degrees}}\\).<\/p>\n<p style=\"text-align: center; overflow-y: hidden; overflow-x: auto;\">\\(120\\text{ degrees}\u00d7\\frac{\u03c0\\text{ radians}}{180\\text{ degrees}}=\\frac{120\\pi}{180}\\text{ radians}=\\frac{2}{3}\\pi\\text{ radians}\\)<\/p>\n<p>How do we convert from radians to degrees? It is very straightforward to derive the conversion factor for radians to degrees.<\/p>\n<p style=\"text-align: center;\">\\(360\\text{ degrees}=2\\pi \\text{ radians}\\)<\/p>\n<p style=\"text-align: center;\">\\(180\\text{ degrees}=\\pi\\text{ radians}\\)<\/p>\n<p>This time, we want the radians unit to end up in the denominator so that when we multiply our number of radians by the conversion factor, the \u201cradians\u201d units cancel each other and leave us with only degrees.<\/p>\n<p style=\"text-align: center;\">\\(\\frac{180\\text{ degrees}}{\u03c0 \\text{ radians}}=\\frac{\u03c0\\text{ radians}}{\u03c0\\text{ radians}}\\)<\/p>\n<p style=\"text-align: center;\">\\(\\frac{180\\text{ degrees}}{\u03c0\\text{ radians}}=1\\)<\/p>\n<p>Just like before, we can now use this conversion factor to take a number of radians and change them into degrees.<\/p>\n<p style=\"text-align: center;\"><strong>Our constant for converting radians to degrees is<\/strong> \\(\\mathbf{\\frac{180\\text{ degrees}}{\u03c0\\text{ radians}}}\\).<\/p>\n<p>As an example, let\u2019s now convert \\(\\frac{5\u03c0}{4}\\) radians to degrees. We multiply our \\(\\frac{5\u03c0}{4}\\) radians by the conversion factor \\(\\frac{180\\text{ degrees}}{\u03c0\\text{ radians}}\\) to eliminate the unit \u201cradians\u201d. From there, the \u03c0\u2019s in the numerator and denominator cancel each other, and a little arithmetic leaves us with our solution, 225\u00b0.<\/p>\n<p style=\"text-align: center; overflow-y: hidden; overflow-x: auto;\">\\(\\frac{5\u03c0}{4}\\text{ radians}\u00d7 \\frac{180\\text{ degrees}}{\u03c0\\text{ radians}}=\\frac{5\u03c0\\times180}{4\\times\u03c0}\\text{ degrees}=225\\text{ degrees}\\)<\/p>\n<h2 class=\"pt-page\"><span id=\"What_are_polar_coordinates\" class=\"m-toc-anchor\"><\/span>What are polar coordinates?<\/h2>\n<p>In the same way that we usually use ordered pairs \\((x,y)\\) to describe points on the Cartesian plane, we can also describe points using the polar coordinates \\((r,\u03b8)\\). The lowercase <em>r<\/em> is a parameter specifying how far away the point is from the origin, and the Greek letter (pronounced \u201cthey-ta\u201d) specifies at which angle the point is from the positive <em>x<\/em>-axis. Usually, we don\u2019t need to use polar coordinates until we get into content from Calculus II, but it can be helpful to see that this is one application for which we use radians in mathematics.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-71468\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/polar-coordinates.png\" alt=\"polar coordinates\" width=\"327.2\" height=\"287.2\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/polar-coordinates.png 818w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/polar-coordinates-300x263.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/polar-coordinates-768x674.png 768w\" sizes=\"(max-width: 818px) 100vw, 818px\" \/><\/p>\n<h3><span id=\"Using_the_Correct_Mode_in_Your_Calculator\" class=\"m-toc-anchor\"><\/span>Using the Correct Mode in Your Calculator<\/h3>\n<p>Scientific calculators are programmed to perform many different functions, including working with both degrees and radians. However, they can only process in terms of one or the other at a single time. If you are dealing with degrees, it is important to make sure that your calculator is in \u201cdegrees\u201d mode first.<\/p>\n<ul>\n<li>For Texas Instruments calculators, press the [MODE] button, then use the arrow keys to highlight DEGREE, and press [ENTER].<\/li>\n<li>For Casio calculators, press [SHIFT] and then [MODE] to access Setup, then press 3 to begin working in degrees.<\/li>\n<\/ul>\n<div id=\"pqs\"><\/div>\n<p>To put your calculator in \u201cradians\u201d mode, follow these similar steps.<\/p>\n<ul>\n<li>For Texas Instruments, press the [MODE] button, then use the arrow keys to highlight RAD, and press [ENTER].<\/li>\n<li>For Casio, press [SHIFT] then [MODE], and finally press 4 to begin working in radians.<\/li>\n<\/ul>\n<a href=\"https:\/\/www.mometrix.com\/university\/mathcr\/?utm_source=academy&amp;utm_medium=inline&amp;utm_campaign=academy-mu-ads&amp;utm_content=mathcr-test\" class=\"class_names\" style=\"color:black;\" onclick=\"_paq.push(['trackEvent', 'Course Button', 'Course Click', 'MathPlacement Course Click']);\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-57671 size-full\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/imcr20-New.png\" alt=\"Click here for 20% off of Mometrix Math College Readiness Online Course. Use code: IMCR20\" width=\"728\" height=\"90\" \/><\/a>\n<h2 class=\"pt-page\"><span id=\"Degrees_and_Radians_Sample_Questions\" class=\"m-toc-anchor\"><\/span>Degrees and Radians Sample Questions<\/h2>\n<p>Here are a few sample questions going over degrees and radians.<br \/>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nConvert \\(\\pi\\) radians to degrees. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">90\u00b0<\/div><div class=\"PQ\"  id=\"PQ-1-2\">120\u00b0<\/div><div class=\"PQ\"  id=\"PQ-1-3\">150\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">180\u00b0<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p style=\"text-align: center; line-height: 65px\">\\(\\pi\\text{ radians}\\times\\dfrac{180\\text{ degrees}}{\\pi\\text{ radians}}\\)\\(\\: =\\dfrac{180\\pi}{\\pi}\\text{ degrees}=180\u00b0\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nConvert 30\u00b0 to radians.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\(\\frac{1}{4} \\pi\\text{ radians}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(\\frac{1}{8} \\pi\\text{ radians}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-3\">\\(\\frac{1}{6} \\pi\\text{ radians}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(\\frac{1}{3} \\pi\\text{ radians}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p style=\"text-align: center; line-height: 65px\">\\(30\\text{ degrees}=\\dfrac{\\pi\\text{ radians}}{180\\text{ degrees}}\\)\\(\\:=\\dfrac{30 \\pi}{180}\\text{ radians}=\\dfrac{1}{6} \\pi\\text{ radians}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nConvert \\(\\large{\\frac{3 \\pi}{2}}\\) radians to degrees.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">150\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">270\u00b0<\/div><div class=\"PQ\"  id=\"PQ-3-3\">330\u00b0<\/div><div class=\"PQ\"  id=\"PQ-3-4\">360\u00b0<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p style=\"text-align: center; line-height: 65px\">\\(\\dfrac{3 \\pi}{2}\\text{ radians}\\times\\dfrac{180\\text{ degrees}}{\\pi\\text{ radians}}\\)\\(\\: =\\dfrac{3 \\pi\\times180}{2 \\pi}\\text{ degrees}=270\\text{ degrees}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nConvert 45\u00b0 to radians.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">\\(\\frac{1}{4}\\pi\\text{ radians}\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(\\frac{1}{2}\\pi\\text{ radians}\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(\\frac{1}{6}\\pi\\text{ radians}\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(\\frac{1}{3}\\pi\\text{ radians}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p style=\"text-align: center; line-height: 65px\">\\(45\\text{ degrees}\\times\\dfrac{\\pi\\text{ radians}}{180\\text{ degrees}}\\)\\(\\:=\\dfrac{45\\pi}{180}\\text{ radians}=\\dfrac{1}{4}\\pi\\text{ radians}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nDetermine how the angle \\(\\large{\\frac{7}{8}}\\normalsize{\\pi}\\) radians is classified.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">Acute<\/div><div class=\"PQ\"  id=\"PQ-5-2\">Right<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">Obtuse<\/div><div class=\"PQ\"  id=\"PQ-5-4\">Reflex<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>We can determine this in two ways.<\/p>\n<p>First, we can convert \\(\\large{\\frac{7}{8}}\\normalsize{\\pi}\\) radians to degrees and then refer to the angle guide presented earlier. This is equivalent to 157.5\u00b0, and since that value is between 90-180\u00b0, we see that it is obtuse.<\/p>\n<p style=\"text-align: center; line-height: 55px\">\\(\\large{\\frac{7}{8}}\\normalsize{\\pi \\text{ radians }\\times}\\large{\\frac{180\\text{ degrees}}{\\pi \\text{ radians}}}\\)\\(\\: = \\large{\\frac{7\\pi \\times 180}{8\\pi}}\\normalsize{\\text{ degrees}=157.5\u00b0}\\)<\/p>\n<p>We can also determine that the angle is obtuse without converting to degrees. Remember that since \\(2\\pi= 360\\text{ degrees}\\), then we can easily determine by division that \\(\\pi=180\\text{ degrees}\\), and \\(2\\pi=90\\text{ degrees}\\). Since \\(\\frac{7}{8}\\pi\\) is clearly between \\(\\frac{\\pi}{2}\\) and \\(\\pi\\), we see that it is an obtuse angle.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/p>\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/math-sample-questions\/\">Return to Math Sample Questions<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What are Angles? We use degrees as units of measurement for angles, and precisely determining how wide or narrow they are. The small circle symbol \u201c\u00b0&#8221; is used following a number to denote that degrees are being represented. Note the following classifications: An acute angle is between 0-90\u00b0 A right angle is 90\u00b0 An obtuse &#8230; <a title=\"Degrees and Radians Overview\" class=\"read-more\" href=\"https:\/\/www.mometrix.com\/academy\/degrees-and-radians\/\" aria-label=\"Read more about Degrees and Radians Overview\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-71447","1":"page","2":"type-page","3":"status-publish","5":"page_category-math-advertising-group","6":"page_category-math-non-video-pages","7":"page_type-topic-overview","8":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/71447","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=71447"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/71447\/revisions"}],"predecessor-version":[{"id":281915,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/71447\/revisions\/281915"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=71447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}