{"id":210,"date":"2016-01-10T16:13:40","date_gmt":"2016-01-10T21:13:40","guid":{"rendered":"https:\/\/trigonography.com\/?p=210"},"modified":"2022-06-25T01:58:43","modified_gmt":"2022-06-25T06:58:43","slug":"trig-sums-with-angles-in-arithmetic-progression","status":"publish","type":"post","link":"https:\/\/trigonography.com\/?p=210","title":{"rendered":"Trig Sums with Angles in Arithmetic Progression"},"content":{"rendered":"<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><a href=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/01\/trigonograph-sincosarithmeticprogression@2x.png\" rel=\"attachment wp-att-211\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/01\/trigonograph-sincosarithmeticprogression@2x.png\" alt=\"trigonograph-sincosarithmeticprogression@2x\" class=\"wp-image-211\" width=\"650\" height=\"600\" srcset=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/01\/trigonograph-sincosarithmeticprogression@2x.png 650w, https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/01\/trigonograph-sincosarithmeticprogression@2x-300x277.png 300w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a><\/figure>\n<\/div>\n\n\n<div class=\"eqn-box\" style=\"margin-bottom: 20pt; font-size:12pt;\">$$\\begin{align}<br>\\sum_{k=0}^{n-1}\\;\\sin\\,2k\\theta \\;=\\; \\frac{\\sin\\,n\\theta}{\\sin\\theta}\\cdot\\sin\\,(n-1)\\theta \\\\[8pt]<br>\\sum_{k=0}^{n-1}\\;\\cos\\,2k\\theta \\;=\\; \\frac{\\sin\\,n\\theta}{\\sin\\theta}\\cdot\\cos\\,(n-1)\\theta<br>\\end{align}$$<\/div>\n","protected":false},"excerpt":{"rendered":"<p>$$\\begin{align}\\sum_{k=0}^{n-1}\\;\\sin\\,2k\\theta \\;=\\; \\frac{\\sin\\,n\\theta}{\\sin\\theta}\\cdot\\sin\\,(n-1)\\theta \\\\[8pt]\\sum_{k=0}^{n-1}\\;\\cos\\,2k\\theta \\;=\\; \\frac{\\sin\\,n\\theta}{\\sin\\theta}\\cdot\\cos\\,(n-1)\\theta\\end{align}$$<\/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-210","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/210","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=210"}],"version-history":[{"count":4,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/210\/revisions"}],"predecessor-version":[{"id":1205,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/210\/revisions\/1205"}],"wp:attachment":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}