{"id":2788,"date":"2025-08-13T18:40:30","date_gmt":"2025-08-13T18:40:30","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2788"},"modified":"2025-10-22T20:02:51","modified_gmt":"2025-10-22T20:02:51","slug":"parametric-functions-and-vectors-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/parametric-functions-and-vectors-background-youll-need-2\/","title":{"raw":"Parametric Functions and Vectors: Background You'll Need 2","rendered":"Parametric Functions and Vectors: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Use inverse tangent to find an unknown angle<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p data-start=\"1713\" data-end=\"1863\">When you know the sides of a right triangle, you can find the angle using the inverse tangent function, written as [latex]\\tan^{-1}[\/latex] or arctan.<\/p>\r\n\r\n<section class=\"textbox example\" aria-label=\"Example\">\r\n<p data-start=\"1879\" data-end=\"2027\">In a right triangle, the opposite side is 4 units long and the adjacent side is 3 units long.<br data-start=\"1972\" data-end=\"1975\" \/>Find the measure of the angle [latex]\\theta[\/latex].<\/p>\r\n<p data-start=\"2029\" data-end=\"2132\">Use the definition of tangent:<br data-start=\"2059\" data-end=\"2062\" \/>[latex]\\tan(\\theta) = \\dfrac{\\text{opposite}}{\\text{adjacent}}[\/latex]<\/p>\r\n<p data-start=\"2134\" data-end=\"2190\">Substitute:<br data-start=\"2145\" data-end=\"2148\" \/>[latex]\\tan(\\theta) = \\dfrac{4}{3}[\/latex]<\/p>\r\n<p data-start=\"2192\" data-end=\"2278\">Take the inverse tangent:<br data-start=\"2217\" data-end=\"2220\" \/>[latex]\\theta = \\tan^{-1}\\left(\\dfrac{4}{3}\\right)[\/latex]<\/p>\r\n<p data-start=\"2280\" data-end=\"2422\">Use a calculator in degree mode:<br data-start=\"2312\" data-end=\"2315\" \/>[latex]\r\n\\begin{align}\r\n\\theta &amp;\\approx \\tan^{-1}(1.3333) \\\\\r\n\\theta &amp;\\approx 53.13^\\circ\r\n\\end{align}\r\n[\/latex]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313901[\/ohm_question]<\/section><section class=\"textbox proTip\" aria-label=\"Pro Tip\">Make sure your calculator is in the correct mode (degrees or radians).<\/section><section class=\"textbox interact\" aria-label=\"Interact\">\r\n<p data-start=\"2772\" data-end=\"2794\"><strong>On a TI-84 Calculator:<\/strong><\/p>\r\n\r\n<ol data-start=\"2795\" data-end=\"2921\">\r\n \t<li data-start=\"2795\" data-end=\"2831\">\r\n<p data-start=\"2798\" data-end=\"2831\">Press <code data-start=\"2804\" data-end=\"2810\">MODE<\/code> \u2192 set to <code data-start=\"2820\" data-end=\"2828\">DEGREE<\/code>.<\/p>\r\n<\/li>\r\n \t<li data-start=\"2832\" data-end=\"2878\">\r\n<p data-start=\"2835\" data-end=\"2878\">Type <code data-start=\"2840\" data-end=\"2845\">2ND<\/code> \u2192 <code data-start=\"2848\" data-end=\"2853\">TAN<\/code> \u2192 <code data-start=\"2856\" data-end=\"2865\">(height \u00f7 width)<\/code> \u2192 <code data-start=\"2868\" data-end=\"2875\">ENTER<\/code>.<\/p>\r\n<\/li>\r\n<\/ol>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Use inverse tangent to find an unknown angle<\/span><\/li>\n<\/ul>\n<\/section>\n<p data-start=\"1713\" data-end=\"1863\">When you know the sides of a right triangle, you can find the angle using the inverse tangent function, written as [latex]\\tan^{-1}[\/latex] or arctan.<\/p>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p data-start=\"1879\" data-end=\"2027\">In a right triangle, the opposite side is 4 units long and the adjacent side is 3 units long.<br data-start=\"1972\" data-end=\"1975\" \/>Find the measure of the angle [latex]\\theta[\/latex].<\/p>\n<p data-start=\"2029\" data-end=\"2132\">Use the definition of tangent:<br data-start=\"2059\" data-end=\"2062\" \/>[latex]\\tan(\\theta) = \\dfrac{\\text{opposite}}{\\text{adjacent}}[\/latex]<\/p>\n<p data-start=\"2134\" data-end=\"2190\">Substitute:<br data-start=\"2145\" data-end=\"2148\" \/>[latex]\\tan(\\theta) = \\dfrac{4}{3}[\/latex]<\/p>\n<p data-start=\"2192\" data-end=\"2278\">Take the inverse tangent:<br data-start=\"2217\" data-end=\"2220\" \/>[latex]\\theta = \\tan^{-1}\\left(\\dfrac{4}{3}\\right)[\/latex]<\/p>\n<p data-start=\"2280\" data-end=\"2422\">Use a calculator in degree mode:<br data-start=\"2312\" data-end=\"2315\" \/>[latex]\\begin{align}  \\theta &\\approx \\tan^{-1}(1.3333) \\\\  \\theta &\\approx 53.13^\\circ  \\end{align}[\/latex]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313901\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313901&theme=lumen&iframe_resize_id=ohm313901&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox proTip\" aria-label=\"Pro Tip\">Make sure your calculator is in the correct mode (degrees or radians).<\/section>\n<section class=\"textbox interact\" aria-label=\"Interact\">\n<p data-start=\"2772\" data-end=\"2794\"><strong>On a TI-84 Calculator:<\/strong><\/p>\n<ol data-start=\"2795\" data-end=\"2921\">\n<li data-start=\"2795\" data-end=\"2831\">\n<p data-start=\"2798\" data-end=\"2831\">Press <code data-start=\"2804\" data-end=\"2810\">MODE<\/code> \u2192 set to <code data-start=\"2820\" data-end=\"2828\">DEGREE<\/code>.<\/p>\n<\/li>\n<li data-start=\"2832\" data-end=\"2878\">\n<p data-start=\"2835\" data-end=\"2878\">Type <code data-start=\"2840\" data-end=\"2845\">2ND<\/code> \u2192 <code data-start=\"2848\" data-end=\"2853\">TAN<\/code> \u2192 <code data-start=\"2856\" data-end=\"2865\">(height \u00f7 width)<\/code> \u2192 <code data-start=\"2868\" data-end=\"2875\">ENTER<\/code>.<\/p>\n<\/li>\n<\/ol>\n<\/section>\n","protected":false},"author":67,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":520,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2788"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2788\/revisions"}],"predecessor-version":[{"id":4823,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2788\/revisions\/4823"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/520"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2788\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2788"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2788"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2788"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2788"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}