{"id":18,"date":"2004-04-04T10:55:05","date_gmt":"2004-04-04T10:55:05","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=18"},"modified":"2007-10-31T14:59:51","modified_gmt":"2007-10-31T14:59:51","slug":"trig-ratios","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=18","title":{"rendered":"Trig Ratios"},"content":{"rendered":"<p>A level syllabuses these days expect you to remember the exact values of sin cos and tan of certain angles. <img src='\/maths\/latexrender\/pictures\/996381aca753da6c2a05dbe8208b9789.gif' title='\\sin 30^\\circ' alt='\\sin 30^\\circ' align=absmiddle> is easy enough as the calculator will give you the exact answer, but unless you know roughly what <img src='\/maths\/latexrender\/pictures\/4818558b83eed5665572c62feed0cf7c.gif' title='\\sin 60^\\circ' alt='\\sin 60^\\circ' align=absmiddle> should be then the calculator will be no help.<\/p>\n<p>But, help is at hand \ud83d\ude00 Memorising formulae is easier when there&#8217;s a pattern and the following table gives such a pattern.<\/p>\n<p><img src='\/maths\/latexrender\/pictures\/948e8ef1910873851d384a9ea83e9d0b.gif' title='\\begin{array}{|c|c|c|c|c|c|} \\hline \\theta &amp; 0^\\circ &amp; 30^\\circ &amp; 45^{\\circ} &amp; 60^\\circ &amp; 90^\\circ \\\\ \\hline&#10;\\begin{array}{c}&#10;\\\\&#10;\\sin \\theta&#10;\\\\ \\\\&#10;\\end{array}&#10; &amp; \\dfrac{\\sqrt{0}}{2} &amp; \\dfrac{\\sqrt{1}}{2} &amp; \\dfrac{\\sqrt{2}}{2} &amp; \\dfrac{\\sqrt{3}}{2} &amp; \\dfrac{\\sqrt{4}}{2} \\\\ \\hline&#10;\\begin{array}{c}&#10;\\\\&#10;\\cos \\theta&#10;\\\\ \\\\&#10;\\end{array}&#10;&amp; \\dfrac{\\sqrt{4}}{2} &amp; \\dfrac{\\sqrt{3}}{2} &amp; \\dfrac{\\sqrt{2}}{2} &amp; \\dfrac{\\sqrt{1}}{2} &amp; \\dfrac{\\sqrt{0}}{2} \\\\ \\hline&#10;\\end{array}' alt='\\begin{array}{|c|c|c|c|c|c|} \\hline \\theta &amp; 0^\\circ &amp; 30^\\circ &amp; 45^{\\circ} &amp; 60^\\circ &amp; 90^\\circ \\\\ \\hline&#10;\\begin{array}{c}&#10;\\\\&#10;\\sin \\theta&#10;\\\\ \\\\&#10;\\end{array}&#10; &amp; \\dfrac{\\sqrt{0}}{2} &amp; \\dfrac{\\sqrt{1}}{2} &amp; \\dfrac{\\sqrt{2}}{2} &amp; \\dfrac{\\sqrt{3}}{2} &amp; \\dfrac{\\sqrt{4}}{2} \\\\ \\hline&#10;\\begin{array}{c}&#10;\\\\&#10;\\cos \\theta&#10;\\\\ \\\\&#10;\\end{array}&#10;&amp; \\dfrac{\\sqrt{4}}{2} &amp; \\dfrac{\\sqrt{3}}{2} &amp; \\dfrac{\\sqrt{2}}{2} &amp; \\dfrac{\\sqrt{1}}{2} &amp; \\dfrac{\\sqrt{0}}{2} \\\\ \\hline&#10;\\end{array}' align=absmiddle><\/p>\n<p>Isn&#8217;t that amazing! I only came across this a few years ago but apparently it&#8217;s been around at least since the 1950&#8217;s.<\/p>\n<p>What about tan? Since <img src='\/maths\/latexrender\/pictures\/274346f75b4e3b84a700ab0a7da4c262.gif' title='\\tan \\theta = \\dfrac{\\sin \\theta}{\\cos \\theta}' alt='\\tan \\theta = \\dfrac{\\sin \\theta}{\\cos \\theta}' align=absmiddle> you just divide a value from the second row by the one below it (but <i>please<\/i> not for <img src='\/maths\/latexrender\/pictures\/cbb05423d43193dc7a8067a59d4bd316.gif' title='90^\\circ' alt='90^\\circ' align=absmiddle>; see <a href=\"http:\/\/sixthform.info\/maths\/index.php?m=200403#16\" target=\"_blank\">Tuesday 16 March<\/a>). <\/p>\n","protected":false},"excerpt":{"rendered":"<p>A level syllabuses these days expect you to remember the exact values of sin cos and tan of certain angles. is easy enough as the calculator will give you the exact answer, but unless you know roughly what should be then the calculator will be no help. But, help is at hand \ud83d\ude00 Memorising formulae [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-18","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/18","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=18"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/18\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=18"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=18"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=18"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}