{"id":67,"date":"2012-07-17T01:55:52","date_gmt":"2012-07-17T06:55:52","guid":{"rendered":"http:\/\/daylateanddollarshort.com\/bloog\/?p=67"},"modified":"2012-07-17T07:20:44","modified_gmt":"2012-07-17T12:20:44","slug":"proof-with-too-many-words-derivatives-of-sine-and-cosine","status":"publish","type":"post","link":"http:\/\/daylateanddollarshort.com\/bloog\/proof-with-too-many-words-derivatives-of-sine-and-cosine\/","title":{"rendered":"Proof with Too Many Words: Derivatives of Sine and Cosine"},"content":{"rendered":"

I’d like to think that the following constitutes a Proof without Words of the formulas for the derivatives of sine and cosine.<\/p>\n

\"Derivatives<\/a><\/div>\n

Unfortunately, it seems that words may be in order, so I wrote some here: “Calculus-free Derivatives of Sine and Cosine”<\/a>\u00a0… even though, strictly speaking, the proof isn’t entirely calculus-free. (Why we expect the projection of the tangent line to a helix to be tangent to the planar projections of the helix needs justification.)<\/p>\n

But the idea is good for the intuition.<\/p>\n

I even made an interactive illustration<\/a>\u00a0for the Wolfram Demonstrations Project<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

I’d like to think that the following constitutes a Proof without Words of the formulas for the derivatives of sine and cosine. Unfortunately, it seems that words may be in order, so I wrote some here: “Calculus-free Derivatives of Sine and Cosine”\u00a0… even though, strictly speaking, the proof isn’t entirely calculus-free. (Why we expect the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-67","post","type-post","status-publish","format-standard","hentry","category-trigonography"],"_links":{"self":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts\/67","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/comments?post=67"}],"version-history":[{"count":7,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts\/67\/revisions"}],"predecessor-version":[{"id":111,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/posts\/67\/revisions\/111"}],"wp:attachment":[{"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/media?parent=67"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/categories?post=67"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/daylateanddollarshort.com\/bloog\/wp-json\/wp\/v2\/tags?post=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}