{"id":3019,"date":"2023-01-13T17:19:37","date_gmt":"2023-01-13T17:19:37","guid":{"rendered":"http:\/\/mclements.net\/blogWP\/?p=3019"},"modified":"2023-01-13T17:23:32","modified_gmt":"2023-01-13T17:23:32","slug":"slide-rules-trig","status":"publish","type":"post","link":"http:\/\/mclements.net\/blogWP\/index.php\/2023\/01\/13\/slide-rules-trig\/","title":{"rendered":"Slide Rules: Trig"},"content":{"rendered":"<p>Introduction and basics in <a href=\"http:\/\/mclements.net\/blogWP\/index.php\/2023\/01\/12\/slide-rules\/\">Part 1<\/a>. Squares, Cubes and roots in <a href=\"http:\/\/mclements.net\/blogWP\/index.php\/2023\/01\/09\/slide-rule-past-the-basics\/\">Part 2<\/a>. Here we cover trigonometry: sine, cosine and tangent. Not all slide rules have these scales, but when they do they are usually labeled as follows:<\/p>\n<ul>\n<li>S: sine<\/li>\n<li>T: tangent<\/li>\n<li>ST: sine &amp; tangent<\/li>\n<\/ul>\n<p>Notes on these scales:<\/p>\n<h3>Trig Scales<\/h3>\n<p>You don&#8217;t need both sine &amp; cosine, since they are inverse every 1\/4 circle or 90 degrees. That is, for any angle A in degrees, sin(A) = cos(90-A). That&#8217;s why slide rules don&#8217;t have a cosine scale &#8211; it&#8217;s not needed.<\/p>\n<p>Knowing a few key values of sine enables one to quickly estimate many problems (like crosswinds when landing an airplane) in your head. No need for a slide rule, let alone a calculator.<\/p>\n<ul>\n<li>sin(0) = 0<\/li>\n<li>sin(30) = 0.5<\/li>\n<li>sin(45) = 0.707<\/li>\n<li>sin(90) = 1<\/li>\n<\/ul>\n<p>For small angles, sine and tangent are almost the same. Thus many slide rules have an shared ST scale for both, for small angles &#8211; typically less than about 5*. Exactly how close are sine and tangent for small angles?<\/p>\n<ul>\n<li>2 sig figs: 15* &#8211; sin &amp; tan differ by the 2nd sig fig\n<ul>\n<li>sin(15*) = 0.259<\/li>\n<li>tan(15*) = 0.268<\/li>\n<\/ul>\n<\/li>\n<li>3 sig figs: 2* &#8211; sin &amp; tan differ by the 3rd sig fig\n<ul>\n<li>sin(3*) = 0.0523<\/li>\n<li>tan(3*) = 0.0524<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introduction and basics in Part 1. Squares, Cubes and roots in Part 2. Here we cover trigonometry: sine, cosine and tangent. Not all slide rules have these scales, but when they do they are usually labeled as follows: S: sine T: tangent ST: sine &amp; tangent Notes on these scales: Trig Scales You don&#8217;t need &hellip; <a href=\"http:\/\/mclements.net\/blogWP\/index.php\/2023\/01\/13\/slide-rules-trig\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Slide Rules: Trig<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17,2],"tags":[],"class_list":["post-3019","post","type-post","status-publish","format-standard","hentry","category-math","category-tech"],"_links":{"self":[{"href":"http:\/\/mclements.net\/blogWP\/index.php\/wp-json\/wp\/v2\/posts\/3019","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/mclements.net\/blogWP\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/mclements.net\/blogWP\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/mclements.net\/blogWP\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/mclements.net\/blogWP\/index.php\/wp-json\/wp\/v2\/comments?post=3019"}],"version-history":[{"count":3,"href":"http:\/\/mclements.net\/blogWP\/index.php\/wp-json\/wp\/v2\/posts\/3019\/revisions"}],"predecessor-version":[{"id":3023,"href":"http:\/\/mclements.net\/blogWP\/index.php\/wp-json\/wp\/v2\/posts\/3019\/revisions\/3023"}],"wp:attachment":[{"href":"http:\/\/mclements.net\/blogWP\/index.php\/wp-json\/wp\/v2\/media?parent=3019"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/mclements.net\/blogWP\/index.php\/wp-json\/wp\/v2\/categories?post=3019"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/mclements.net\/blogWP\/index.php\/wp-json\/wp\/v2\/tags?post=3019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}