{"id":7587,"date":"2022-09-10T07:23:04","date_gmt":"2022-09-10T07:23:04","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7587"},"modified":"2022-09-10T07:23:04","modified_gmt":"2022-09-10T07:23:04","slug":"inverse-trigonometric-functions-graphs","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/10\/inverse-trigonometric-functions-graphs\/","title":{"rendered":"Inverse Trigonometric&nbsp; Functions Graphs"},"content":{"rendered":"\n<p>There are particularly six inverse trig functions for each\u00a0trigonometry ratio. The inverse of six important trigonometric functions are:<\/p>\n\n\n\n<ul><li>Arcsine<\/li><li>Arccosine<\/li><li>Arctangent<\/li><li>Arccotangent<\/li><li>Arcsecant<\/li><li>Arccosecant<\/li><\/ul>\n\n\n\n<p>Let us discuss all the six important types of inverse trigonometric functions along with its definition, formulas, graphs, properties and solved examples.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Arcsine Function<\/h3>\n\n\n\n<p>Arcsine function is an inverse of the sine function denoted by sin<sup>-1<\/sup><em>x<\/em>. It is represented in the graph as shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2019\/07\/arcsin.png\" alt=\"Arcsine Function Graph\" title=\"Arcsine-Inverse sine Function\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table><tbody><tr><td><strong>Domain<\/strong><\/td><td>-1 \u2264 x \u2264 1<\/td><\/tr><tr><td><strong>Range<\/strong><\/td><td>-\u03c0\/2 \u2264 y \u2264 \u03c0\/2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Arccosine Function<\/h3>\n\n\n\n<p>Arccosine function is the inverse of the cosine function denoted by cos<sup>-1<\/sup><em>x<\/em>. It is represented in the graph as shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2019\/07\/Arccos.png\" alt=\"Arccos Function Graph\" title=\"Arccos\"\/><\/figure>\n\n\n\n<p>Therefore, the inverse of cos function can be expressed as;&nbsp;<strong>y = cos<sup>-1<\/sup>x&nbsp;<\/strong><strong>(arccosine&nbsp;<em>x<\/em>)<\/strong><\/p>\n\n\n\n<p>Domain &amp; Range of arcsine function:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table><tbody><tr><td><strong>Domain<\/strong><\/td><td>-1\u2264x\u22641<\/td><\/tr><tr><td><strong>Range<\/strong><\/td><td>0 \u2264 y \u2264 \u03c0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Arctangent Function<\/h3>\n\n\n\n<p>Arctangent function is the inverse of the tangent function denoted by tan<sup>-1<\/sup><em>x<\/em>. It is represented in the graph as shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2019\/07\/arctan.png\" alt=\"Arctan function Graph\" title=\"Arctan\"\/><\/figure>\n\n\n\n<p>Therefore, the inverse of tangent function can be expressed as;&nbsp;<strong>y = tan<sup>-1<\/sup>x&nbsp;<\/strong><strong>(arctangent&nbsp;<em>x<\/em>)<\/strong><\/p>\n\n\n\n<p>Domain &amp; Range of Arctangent:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table><tbody><tr><td><strong>Domain<\/strong><\/td><td>-\u221e &lt; x &lt; \u221e<\/td><\/tr><tr><td><strong>Range<\/strong><\/td><td>-\u03c0\/2 &lt; y &lt; \u03c0\/2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Arccotangent (Arccot) Function<\/h3>\n\n\n\n<p>Arccotangent function is the inverse of the cotangent function denoted by cot<sup>-1<\/sup><em>x<\/em>. It is represented in the graph as shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2021\/04\/Screenshot-2021-04-23-at-10.09.29.png\" alt=\"Arc cotangent Graph\"\/><\/figure>\n\n\n\n<p>Therefore, the inverse of cotangent function can be expressed as;&nbsp;<strong>y = cot<sup>-1<\/sup>x&nbsp;<\/strong><strong>(arccotangent&nbsp;<em>x<\/em>)<\/strong><\/p>\n\n\n\n<p>Domain &amp; Range of Arccotangent:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table><tbody><tr><td><strong>Domain<\/strong><\/td><td>-\u221e &lt; x &lt; \u221e<\/td><\/tr><tr><td><strong>Range<\/strong><\/td><td>0 &lt; y &lt; \u03c0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Arcsecant Function<\/h3>\n\n\n\n<p><strong>What is arcsecant (arcsec)function?<\/strong>&nbsp;Arcsecant function is the inverse of the secant function denoted by sec<sup>-1<\/sup><em>x<\/em>. It is represented in the graph as shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2019\/07\/arcsecx1.png\" alt=\"Arcsec Function Graph\" title=\"Arcsec\"\/><\/figure>\n\n\n\n<p>Therefore, the inverse of secant function can be expressed as;&nbsp;<strong>y = sec<sup>-1<\/sup>x&nbsp;<\/strong><strong>(arcsecant&nbsp;<em>x<\/em>)<\/strong><\/p>\n\n\n\n<p>Domain &amp; Range of Arcsecant:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table><tbody><tr><td><strong>Domain<\/strong><\/td><td>-\u221e \u2264 x \u2264 -1 or 1 \u2264 x \u2264 \u221e<\/td><\/tr><tr><td><strong>Range<\/strong><\/td><td>0 \u2264 y \u2264 \u03c0, y \u2260 \u03c0\/2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Arccosecant Function<\/h3>\n\n\n\n<p>What is arccosecant (arccsc&nbsp;<em>x<\/em>) function? Arccosecant function is the inverse of the cosecant function denoted by cosec<sup>-1<\/sup><em>x<\/em>. It is represented in the graph as shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2019\/07\/arccscx1.png\" alt=\"Arccsc Function Graph\" title=\"Arccsc\"\/><\/figure>\n\n\n\n<p>Therefore, the inverse of cosecant function can be expressed as;&nbsp;<strong>y = cosec<sup>-1<\/sup>x&nbsp;<\/strong><strong>(arccosecant&nbsp;<em>x<\/em>)<\/strong><\/p>\n\n\n\n<p>Domain &amp; Range of Arccosecant is:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table><tbody><tr><td><strong>Domain<\/strong><\/td><td>-\u221e \u2264 x \u2264 -1 or 1 \u2264 x \u2264 \u221e<\/td><\/tr><tr><td><strong>Range<\/strong><\/td><td>-\u03c0\/2 \u2264 y \u2264 \u03c0\/2, y \u2260 0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Inverse Trigonometric Functions Table<\/h2>\n\n\n\n<p>Let us rewrite here all the inverse trigonometric functions with their notation, definition, domain and range.<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table><tbody><tr><td><strong>Function Name<\/strong><\/td><td><strong>Notation<\/strong><\/td><td><strong>Definition<\/strong><\/td><td><strong>Domain of&nbsp; x<\/strong><\/td><td><strong>Range<\/strong><\/td><\/tr><tr><td>Arcsine or inverse sine<\/td><td>y = sin<sup>-1<\/sup>(x)<\/td><td>x=sin y<\/td><td>\u22121 \u2264 x \u2264 1<\/td><td>\u2212 \u03c0\/2 \u2264 y \u2264 \u03c0\/2-90\u00b0\u2264 y \u2264 90\u00b0<\/td><\/tr><tr><td>Arccosine or inverse cosine<\/td><td>y=cos<sup>-1<\/sup>(x)<\/td><td>x=cos y<\/td><td>\u22121 \u2264 x \u2264 1<\/td><td>0 \u2264 y \u2264 \u03c00\u00b0 \u2264 y \u2264 180\u00b0<\/td><\/tr><tr><td>Arctangent orInverse tangent<\/td><td>y=tan<sup>-1<\/sup>(x)<\/td><td>x=tan y<\/td><td>For all real numbers<\/td><td>\u2212 \u03c0\/2 &lt; y &lt; \u03c0\/2-90\u00b0&lt; y &lt; 90\u00b0<\/td><\/tr><tr><td>Arccotangent orInverse Cot<\/td><td>y=cot<sup>-1<\/sup>(x)<\/td><td>x=cot y<\/td><td>For all real numbers<\/td><td>0 &lt; y &lt; \u03c00\u00b0 &lt; y &lt; 180\u00b0<\/td><\/tr><tr><td>Arcsecant orInverse Secant<\/td><td>y = sec<sup>-1<\/sup>(x)<\/td><td>x=sec y<\/td><td>x \u2264 \u22121 or 1 \u2264 x<\/td><td>0\u2264y&lt;\u03c0\/2 or \u03c0\/2&lt;y\u2264\u03c00\u00b0\u2264y&lt;90\u00b0 or 90\u00b0&lt;y\u2264180\u00b0<\/td><\/tr><tr><td>Arccosecant<\/td><td>y=csc<sup>-1<\/sup>(x)<\/td><td>x=csc y<\/td><td>x \u2264 \u22121 or 1 \u2264 x<\/td><td>\u2212\u03c0\/2\u2264y&lt;0 or 0&lt;y\u2264\u03c0\/2\u221290\u00b0\u2264y&lt;0\u00b0or 0\u00b0&lt;y\u226490\u00b0<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>There are particularly six inverse trig functions for each\u00a0trigonometry ratio. The inverse of six important trigonometric functions are: Arcsine Arccosine Arctangent Arccotangent Arcsecant Arccosecant Let us discuss all the six important types of inverse trigonometric functions along with its definition, formulas, graphs, properties and solved examples. Arcsine Function Arcsine function is an inverse of the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[482],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7587"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=7587"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7587\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7587"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7587"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}