{"id":213494,"date":"2024-02-15T10:27:31","date_gmt":"2024-02-15T16:27:31","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=213494"},"modified":"2026-05-06T10:18:08","modified_gmt":"2026-05-06T15:18:08","slug":"unit-circle-calculator","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/unit-circle-calculator\/","title":{"rendered":"Unit Circle Calculator"},"content":{"rendered":"<p><script src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-mml-chtml.js\"><\/script><\/p>\n<div class=\"ucc-wrap\">\n<div class=\"ucc-calculator\">\n<div class=\"ucc-body\">\n<div class=\"ucc-input-fields\">\n<div class=\"ucc-input-row\" id=\"ucc-angleRow\">\n<div class=\"ucc-input-label\">Angle<\/div>\n<p>          <input type=\"text\" id=\"ucc-angle\" placeholder=\"0\">\n        <\/div>\n<div class=\"ucc-dropdown-row\">\n<div class=\"ucc-dropdown-label\">Unit<\/div>\n<p>          <select id=\"ucc-unit\"><option value=\"deg\">Degrees (\u00b0)<\/option><option value=\"rad\">Radians (rad)<\/option><\/select>\n        <\/div>\n<\/p><\/div>\n<div class=\"ucc-canvas-area\">\n        <canvas id=\"ucc-canvas\" width=\"720\" height=\"720\"><\/canvas>\n      <\/div>\n<div class=\"ucc-results\">\n<div class=\"ucc-result-item\">\n<div class=\"ucc-result-label\"><math><mi>x<\/mi><mfenced><mrow><mi>cos<\/mi><mi>&theta;<\/mi><\/mrow><\/mfenced><\/math><\/div>\n<div class=\"ucc-result-val\" id=\"ucc-cos\">1<\/div>\n<\/p><\/div>\n<div class=\"ucc-result-item\">\n<div class=\"ucc-result-label\"><math><mi>y<\/mi><mfenced><mrow><mi>sin<\/mi><mi>&theta;<\/mi><\/mrow><\/mfenced><\/math><\/div>\n<div class=\"ucc-result-val\" id=\"ucc-sin\">0<\/div>\n<\/p><\/div>\n<div class=\"ucc-result-item\">\n<div class=\"ucc-result-label\"><math><mi>tan<\/mi><mi>&theta;<\/mi><\/math><\/div>\n<div class=\"ucc-result-val\" id=\"ucc-tan\">0<\/div>\n<\/p><\/div>\n<div class=\"ucc-result-item\">\n<div class=\"ucc-result-label\">Quadrant<\/div>\n<div class=\"ucc-result-val\" id=\"ucc-quadrant\">I<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<div style=\"text-align: center; margin-top: -0.3em; margin-bottom: 0.5em; font-size: 80%\">Found a bug? <a class=\"ylist\" href=\"https:\/\/airtable.com\/appgcc1PP0BbzPCbI\/shrb33jgGwb66DWHC?prefill_Test=Unit%20Circle%20Calculator&#038;prefill_Question+Number=0&#038;prefill_Which+Form=Calculator-Feedback&#038;prefill_UP-ID=Calculator-Feedback%20-%20Unit%20Circle%20Calculator%20-%200&#038;hide_Test=true&#038;hide_Which+Form=true&#038;hide_UP-ID=true&#038;hide_Question+Number=true\" target=\"_blank\" rel=\"noopener\">Let us know!<\/a><\/div>\n<p>&nbsp;<br \/>\nKnowing how to use the unit circle is a fundamental skill in trigonometry!<\/p>\n<p>The unit circle is a circle of radius 1 centered at the origin. For any angle \\(\\theta\\) (in degrees or radians), the coordinates of the point on the circle are \\((x,y)=(\\cos\\theta,\\ \\sin\\theta)\\).<\/p>\n<p>Angles are measured from the positive \\(x\\)-axis, counterclockwise positive.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/04\/Unit_circle_angles_color.svg\" alt=\"Unit circle diagram featuring angle measurements in degrees and radians, with corresponding trigonometric ratios of side lengths\" width=\"400\" height=\"400\" class=\"aligncenter size-full wp-image-252515\"  role=\"img\" \/><\/p>\n<h3>Quick References<\/h3>\n<h4 style=\"margin-bottom: 0em\">Full Turn<\/h4>\n<p>One full turn around the circle is \\(360^\\circ\\), which equals \\(2\\pi\\) radians.<\/p>\n<h4 style=\"margin-bottom: 0em\">Quadrants<\/h4>\n<p>The sign pattern of the coordinates follows the quadrant:<\/p>\n<ul>\n<li><span style=\"font-weight: 500\">Quadrant I:<\/span> \\((+,+)\\)<\/li>\n<li><span style=\"font-weight: 500\">Quadrant II:<\/span> \\((-,+)\\)<\/li>\n<li><span style=\"font-weight: 500\">Quadrant III:<\/span> \\((-,-)\\)<\/li>\n<li><span style=\"font-weight: 500\">Quadrant IV:<\/span> \\((+,-)\\)<\/li>\n<\/ul>\n<p>On the unit circle, the Pythagorean identity always holds:<\/p>\n<p style=\"text-align: center\">\\(\\sin^2\\theta+\\cos^2\\theta=1\\)<\/p>\n<p>Tangent is defined by \\(\\tan\\theta=\\dfrac{\\sin\\theta}{\\cos\\theta}\\) whenever \\(\\cos\\theta\\neq 0\\).<\/p>\n<h4 style=\"margin-bottom: 0em\">Converting Units<\/h4>\n<p>To convert units, multiply degrees by \\(\\frac{\\pi}{180}\\) to get radians or multiply radians by \\(\\frac{180}{\\pi}\\) to get degrees:<\/p>\n<p style=\"text-align: center\">\\(\\theta_{\\text{rad}}=\\theta^\\circ\\cdot\\dfrac{\\pi}{180}\\)<\/p>\n<p style=\"text-align: center\">\\(\\theta^\\circ=\\theta_{\\text{rad}}\\cdot\\dfrac{180}{\\pi}\\)<\/p>\n<div class=\"home-buttons2\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/unit-circles-and-standard-position\/\">Learn More About Unit Circles Here!<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Angle Unit Degrees (\u00b0)Radians (rad) xcos&theta; 1 ysin&theta; 0 tan&theta; 0 Quadrant I Found a bug? Let us know! &nbsp; Knowing how to use the unit circle is a fundamental skill in trigonometry! The unit circle is a circle of radius 1 centered at the origin. For any angle (in degrees or radians), the coordinates &#8230; <a title=\"Unit Circle Calculator\" class=\"read-more\" href=\"https:\/\/www.mometrix.com\/academy\/unit-circle-calculator\/\" aria-label=\"Read more about Unit Circle Calculator\">Read more<\/a><\/p>\n","protected":false},"author":68,"featured_media":265930,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-213494","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_type-calculator"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/213494","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/68"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=213494"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/213494\/revisions"}],"predecessor-version":[{"id":293351,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/213494\/revisions\/293351"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/265930"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=213494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}