{"id":1079,"date":"2017-08-12T00:55:06","date_gmt":"2017-08-12T05:55:06","guid":{"rendered":"https:\/\/trigonography.com\/?p=1079"},"modified":"2022-06-24T23:21:50","modified_gmt":"2022-06-25T04:21:50","slug":"a-divided-angle-tangent-inequality","status":"publish","type":"post","link":"https:\/\/trigonography.com\/?p=1079","title":{"rendered":"A Divided-Angle Tangent Inequality"},"content":{"rendered":"<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><a href=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2017\/08\/mse-tannt-vs-ntant.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2017\/08\/mse-tannt-vs-ntant.png\" alt=\"\" width=\"320\" height=\"521\"\/><\/a><\/figure>\n<\/div>\n\n\n<div class=\"eqn-box\" style=\"margin-bottom: 20pt; font-size:12pt\">$$0 &lt; \\theta &lt; \\frac{\\pi}{2}\\quad\\text{and}\\quad 1 &lt; n \\in \\mathbb{N}\\quad\\Rightarrow\\quad \\tan\\theta \\;&gt;\\; n\\;\\tan\\frac{\\theta}{n}$$<\/div>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\" style=\"font-size:16px\"><em style=\"color: gray;\">Motivated by <a href=\"https:\/\/math.stackexchange.com\/q\/2390195\/409\">this question<\/a> on the Mathematics Stack Exchange.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>$$0 &lt; \\theta &lt; \\frac{\\pi}{2}\\quad\\text{and}\\quad 1 &lt; n \\in \\mathbb{N}\\quad\\Rightarrow\\quad \\tan\\theta \\;&gt;\\; n\\;\\tan\\frac{\\theta}{n}$$ Motivated by this question on the Mathematics Stack Exchange.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1079","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/1079","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1079"}],"version-history":[{"count":8,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/1079\/revisions"}],"predecessor-version":[{"id":1177,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/1079\/revisions\/1177"}],"wp:attachment":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1079"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1079"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1079"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}