{"id":535,"date":"2016-06-20T14:24:20","date_gmt":"2016-06-20T19:24:20","guid":{"rendered":"https:\/\/trigonography.com\/?p=535"},"modified":"2022-06-25T01:51:14","modified_gmt":"2022-06-25T06:51:14","slug":"sum-of-sines-sum-of-cosines-sum-of-angles","status":"publish","type":"post","link":"https:\/\/trigonography.com\/?p=535","title":{"rendered":"Sum of Sines, Sum of Cosines, Sum of Angles"},"content":{"rendered":"<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><a href=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/08\/trigonograph-sumofsinescosinesangles.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/08\/trigonograph-sumofsinescosinesangles.png\" alt=\"trigonograph-sumofsinescosinesangles\" width=\"360\" height=\"540\"\/><\/a><\/figure>\n<\/div>\n\n\n<div class=\"eqn-box\" style=\"margin-bottom: 20pt; font-size:12pt;\">$$\\left.\\begin{align}<br>\\sin\\theta + \\sin\\phi &amp;= a \\\\[4pt]<br>\\cos\\theta + \\cos\\phi &amp;= b<br>\\end{align}\\quad\\right\\} \\quad\\Longrightarrow\\quad\\sin\\left(\\theta+\\phi\\right) = \\frac{2ab}{a^2+b^2}$$<\/div>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\" style=\"font-size:16px\">$$a b \\;=\\; 2|\\triangle ABC| \\;=\\; c \\cdot \\frac{c}{2}\\sin\\left(\\alpha+\\beta\\right)<br>\\quad\\Longrightarrow\\quad\\sin\\left(\\alpha + \\beta\\right) = \\frac{2ab}{c^2}$$<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\" style=\"font-size:16px\"><em style=\"color: gray;\"><br><br><br>Motivated by <a href=\"http:\/\/math.stackexchange.com\/q\/1833153\/409\">this question<\/a> on the Mathematics Stack Exchange.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>$$\\left.\\begin{align}\\sin\\theta + \\sin\\phi &amp;= a \\\\[4pt]\\cos\\theta + \\cos\\phi &amp;= b\\end{align}\\quad\\right\\} \\quad\\Longrightarrow\\quad\\sin\\left(\\theta+\\phi\\right) = \\frac{2ab}{a^2+b^2}$$ $$a b \\;=\\; 2|\\triangle ABC| \\;=\\; c \\cdot \\frac{c}{2}\\sin\\left(\\alpha+\\beta\\right)\\quad\\Longrightarrow\\quad\\sin\\left(\\alpha + \\beta\\right) = \\frac{2ab}{c^2}$$ 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-535","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/535","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=535"}],"version-history":[{"count":10,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/535\/revisions"}],"predecessor-version":[{"id":1199,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/535\/revisions\/1199"}],"wp:attachment":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=535"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=535"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}