{"id":614,"date":"2022-08-30T15:04:17","date_gmt":"2022-08-30T15:04:17","guid":{"rendered":"https:\/\/unknownerror.org\/index.php\/2013\/11\/09\/what-is-the-domain-and-range-of-this-fxsecpiex-4-collection-of-common-programming-errors\/"},"modified":"2022-08-30T15:04:17","modified_gmt":"2022-08-30T15:04:17","slug":"what-is-the-domain-and-range-of-this-fxsecpiex-4-collection-of-common-programming-errors","status":"publish","type":"post","link":"https:\/\/unknownerror.org\/index.php\/2022\/08\/30\/what-is-the-domain-and-range-of-this-fxsecpiex-4-collection-of-common-programming-errors\/","title":{"rendered":"What is the domain and range of this: f(x)=sec((pie*x)\/4)?-Collection of common programming errors"},"content":{"rendered":"<ul>\n<li>I&#8217;m going to assume you mean &#8220;pi&#8221; and not &#8220;pie&#8221;, because I don&#8217;t know how to take the secant of a round, baked dessert. sec is the secant function. If you don&#8217;t know your six trigonometry functions, then I don&#8217;t know how you could answer this.\n<p>f(x) = sec(\u03c0 x \/ 4) = 1 \/ cos(\u03c0 x \/ 4), so this is undefined when cos(\u03c0 x \/ 4) = 0. Since cos(\u03c0\/2), cos(3\u03c0\/2), etc. = 0, this means the function is undefined for x = \u00b11, \u00b13, \u00b15, \u00b17&#8230; So the domain is &#8220;all real numbers except the odd integers&#8221;.<\/p>\n<\/li>\n<li>You did not mention that this is a real function, but I a considering it as a real function: sec((pie*x)\/4) = 1\/(cos((pie*x)\/4)) value of cosA is 0 when A is = (2n+1)(pie\/2) hence (pie*x)\/4 != (2n+1)(pie\/2) x\/2 != (2n+1) x != 2(2n+1) therefore the domain of f(x) is oll real nos except the doubles of odd numbers: D f(x) = R &#8211; {2(2n+1) : n is an integer} R f(x) = R &#8211; (-1,1) Note: Range of sec(x) is always from minus infinity to minus one and from plus one to plus infinity. As for &#8220;sec&#8221; it is just a function of the angle and equivalent to the ratio = hypotenuse\/(adjacent sid of the angle)\n<p>(in a right angle triangle.)<\/p>\n<\/li>\n<\/ul>\n<p id=\"rop\"><small>Originally posted 2013-11-09 21:07:42. <\/small><\/p>","protected":false},"excerpt":{"rendered":"<p>I&#8217;m going to assume you mean &#8220;pi&#8221; and not &#8220;pie&#8221;, because I don&#8217;t know how to take the secant of a round, baked dessert. sec is the secant function. If you don&#8217;t know your six trigonometry functions, then I don&#8217;t know how you could answer this. f(x) = sec(\u03c0 x \/ 4) = 1 \/ [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-614","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/posts\/614","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/comments?post=614"}],"version-history":[{"count":0,"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/posts\/614\/revisions"}],"wp:attachment":[{"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/media?parent=614"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/categories?post=614"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/tags?post=614"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}