{"id":66832,"date":"2026-10-15T09:20:29","date_gmt":"2026-10-15T06:20:29","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66832"},"modified":"2026-10-15T09:20:29","modified_gmt":"2026-10-15T06:20:29","slug":"trigonometry-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/trigonometry-calculator\/","title":{"rendered":"Trigonometry Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Find sin, cos and tan of an Angle \u2014 or the Angle from a Ratio<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66832\" data-favorite-title=\"Trigonometry\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/trigonometry-calculator\/\" data-favorite-excerpt=\"Calculate sin, cos and tan of any angle in degrees, radians or gradians \u2014 or enter a ratio and find the angle using arcsin, arccos or arctan.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-geometry\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/mathematics\/trigonometry-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66832\" data-post=\"66832\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Calculation mode<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"calculation_mode\"><option value=\"forward\" selected>Angle \u2192 sin, cos, tan<\/option><option value=\"inverse\">Ratio (sin, cos or tan) \u2192 angle<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Angle<\/label><div class=\"term\">\u03b8<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"number\" name=\"angle\" id=\"field-2\" aria-describedby=\"calc-info-2\" placeholder=\"30\" step=\"any\" value=\"30\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit\" aria-label=\"Unit\"><option value=\"deg\" selected>deg<\/option><option value=\"rad\">rad<\/option><option value=\"grad\">grad<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-2\">Any real angle; it does not have to be between 0\u00b0 and 360\u00b0.<\/small><\/div><div class=\"field\" id=\"input-3\" hidden><label for=\"field-4\">Known function<\/label><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"known_function\"><option value=\"sin\" selected>sin \u03b8<\/option><option value=\"cos\">cos \u03b8<\/option><option value=\"tan\">tan \u03b8<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-5\">Ratio value<\/label><div class=\"term\">y<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"ratio_value\" id=\"field-5\" aria-describedby=\"calc-info-5\" placeholder=\"0.5\" step=\"any\" value=\"0.5\"\/><small id=\"calc-info-5\">The value of the chosen function, e.g. 0.5 for sin \u03b8 = 0.5.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66832\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Trigonometric Values<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Sine<\/span><span class=\"result-term\">sin \u03b8<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Cosine<\/span><span class=\"result-term\">cos \u03b8<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Tangent<\/span><span class=\"result-term\">tan \u03b8<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>Angle \u03b8<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"66832\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Trigonometry Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\sin\\theta = \\frac{\\text{opposite}}{\\text{hypotenuse}} \\qquad \\cos\\theta = \\frac{\\text{adjacent}}{\\text{hypotenuse}} \\qquad \\tan\\theta = \\frac{\\sin\\theta}{\\cos\\theta} \\\\ \\theta = \\arcsin y \\qquad \\theta = \\arccos y \\qquad \\theta = \\arctan y \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(\\theta\\) \u2014 the angle, which can be given in degrees, radians or gradians<\/li>\n<li>\\(y\\) \u2014 the known ratio, i.e. the value of \\(\\sin\\theta\\), \\(\\cos\\theta\\) or \\(\\tan\\theta\\)<\/li>\n<li>\\(\\arcsin\\), \\(\\arccos\\), \\(\\arctan\\) \u2014 the inverse trigonometric functions, also written \\(\\sin^{-1}\\), \\(\\cos^{-1}\\), \\(\\tan^{-1}\\)<\/li>\n<\/ul>\n<p>The first line defines the three basic trigonometric functions as ratios of the sides of a right triangle. The second line inverts the process: given a ratio, the inverse functions recover the angle.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Trigonometry \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> find the sine, cosine and tangent of a 30\u00b0 angle (the calculator's default values).<\/p>\n<p>First convert the angle to radians, since the trigonometric functions are defined on the unit circle:<\/p>\n<p>\\[ 30^\\circ \\cdot \\frac{\\pi}{180^\\circ} = \\frac{\\pi}{6} \\approx 0.523599 \\text{ rad} \\]<\/p>\n<p>\\[ \\sin 30^\\circ = 0.5 \\qquad \\cos 30^\\circ \\approx 0.866025 \\qquad \\tan 30^\\circ = \\frac{0.5}{0.866025} \\approx 0.577350 \\]<\/p>\n<p><strong>Result:<\/strong> \\(\\sin\\theta = 0.5\\), \\(\\cos\\theta \\approx 0.866025\\), \\(\\tan\\theta \\approx 0.577350\\).<\/p>\n<p><strong>Inverse example:<\/strong> if you know that \\(\\sin\\theta = 0.5\\), switch the mode to \"Ratio (sin, cos or tan) \u2192 angle\", choose sin \u03b8 and enter 0.5. The calculator returns the principal angle \\(\\theta = \\arcsin(0.5) = 30^\\circ \\approx 0.523599\\) rad.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>In the <strong>Calculation mode<\/strong> dropdown, choose <em>Angle \u2192 sin, cos, tan<\/em> if you know the angle, or <em>Ratio (sin, cos or tan) \u2192 angle<\/em> if you know one of the ratios.<\/li>\n<li>For the forward mode: enter the angle in the <strong>Angle<\/strong> field and pick its unit (deg, rad or grad) from the <strong>Unit<\/strong> dropdown. Any real number is accepted \u2014 the angle does not need to lie between 0\u00b0 and 360\u00b0.<\/li>\n<li>For the inverse mode: select which ratio you know in <strong>Known function<\/strong> (sin \u03b8, cos \u03b8 or tan \u03b8) and enter its value in <strong>Ratio value<\/strong>.<\/li>\n<li>Read the results: the calculator shows \\(\\sin\\theta\\), \\(\\cos\\theta\\), \\(\\tan\\theta\\) and the angle expressed in degrees, radians and gradians.<\/li>\n<\/ol>\n<h2>What Are Sine, Cosine and Tangent?<\/h2>\n<p>Trigonometry connects angles to ratios of lengths. In a right triangle, the sine of an acute angle is the length of the side opposite the angle divided by the hypotenuse; the cosine is the adjacent side divided by the hypotenuse; and the tangent is the opposite side divided by the adjacent side. These definitions extend beyond right triangles through the unit circle: if a point on a circle of radius 1 makes an angle \\(\\theta\\) with the positive x-axis, then its coordinates are \\((\\cos\\theta, \\sin\\theta)\\).<\/p>\n<p>This circular definition works for <em>any<\/em> angle \u2014 negative, larger than 360\u00b0, or expressed in radians or gradians. The tangent has a simpler identity worth remembering: \\(\\tan\\theta = \\sin\\theta \/ \\cos\\theta\\). It grows without bound as \\(\\cos\\theta\\) approaches zero, which is why the tangent is undefined at 90\u00b0, 270\u00b0, and generally at \\(90^\\circ + k \\cdot 180^\\circ\\).<\/p>\n<p>The inverse functions run the logic backwards. If you know, for example, that \\(\\sin\\theta = 0.5\\), then \\(\\theta = \\arcsin(0.5) = 30^\\circ\\). This is essential in geometry (finding an angle from side lengths), physics (projectile motion, waves) and engineering (signal analysis, AC circuits). The <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/quadratic-mean-calculator-root-mean-square\/\">root mean square<\/a> of a sinusoidal signal, for instance, relies on values of \\(\\sin\\theta\\) and \\(\\cos\\theta\\).<\/p>\n<p>Trigonometric functions also appear far outside geometry. Complex numbers are written in polar form as \\(r(\\cos\\theta + i\\sin\\theta)\\), which is why tools like the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/complex-conjugate\/\">complex conjugate<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/complex-root\/\">complex root<\/a> calculators involve angles and radii in their computations.<\/p>\n<h2>Common Values Reference Table<\/h2>\n<table>\n<thead>\n<tr>\n<th>\u03b8 (degrees)<\/th>\n<th>\u03b8 (radians)<\/th>\n<th>sin \u03b8<\/th>\n<th>cos \u03b8<\/th>\n<th>tan \u03b8<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0\u00b0<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>30\u00b0<\/td>\n<td>\u03c0\/6<\/td>\n<td>1\/2<\/td>\n<td>\u221a3\/2<\/td>\n<td>\u221a3\/3<\/td>\n<\/tr>\n<tr>\n<td>45\u00b0<\/td>\n<td>\u03c0\/4<\/td>\n<td>\u221a2\/2<\/td>\n<td>\u221a2\/2<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>60\u00b0<\/td>\n<td>\u03c0\/3<\/td>\n<td>\u221a3\/2<\/td>\n<td>1\/2<\/td>\n<td>\u221a3<\/td>\n<\/tr>\n<tr>\n<td>90\u00b0<\/td>\n<td>\u03c0\/2<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>undefined<\/td>\n<\/tr>\n<tr>\n<td>180\u00b0<\/td>\n<td>\u03c0<\/td>\n<td>0<\/td>\n<td>\u22121<\/td>\n<td>0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li><strong>Principal values only.<\/strong> Every ratio corresponds to infinitely many angles. In inverse mode the calculator returns the principal value: \\(\\arcsin\\) and \\(\\arctan\\) give results in \u221290\u00b0\u202690\u00b0, while \\(\\arccos\\) gives results in 0\u00b0\u2026180\u00b0. Other solutions follow from the identities \\(\\sin\\theta = \\sin(180^\\circ - \\theta)\\) and \\(\\cos\\theta = \\cos(360^\\circ - \\theta)\\), plus adding any multiple of 360\u00b0.<\/li>\n<li><strong>Range of sine and cosine.<\/strong> Since \\(\\sin\\theta\\) and \\(\\cos\\theta\\) always lie between \u22121 and 1, the calculator rejects ratio values outside this interval for these two functions. The tangent has no such restriction \u2014 any real ratio is valid.<\/li>\n<li><strong>Undefined tangent.<\/strong> When \\(\\cos\\theta = 0\\) (at 90\u00b0 + k\u00b7180\u00b0), the tangent does not exist and the calculator reports it as undefined rather than returning an enormous number.<\/li>\n<li><strong>Rounding.<\/strong> Results are rounded to 6 decimal places, and values that differ from zero only by floating-point noise (for example \\(\\sin 180^\\circ\\) computed as 10\u207b\u00b9\u2076) are displayed as exactly 0.<\/li>\n<li><strong>Unit awareness.<\/strong> Always check the <strong>Unit<\/strong> dropdown before entering an angle. Entering 3.14 while the unit is set to degrees will give a very different answer than 3.14 radians. Recall that \\(180^\\circ = \\pi\\) radians = 200 gradians.<\/li>\n<\/ul>\n<h2>Practical Tips<\/h2>\n<p>When solving triangle problems, decide first whether you know an angle or a ratio. If two sides of a right triangle are known, form the appropriate ratio (opposite\/hypotenuse, adjacent\/hypotenuse or opposite\/adjacent) and use inverse mode to recover the angle. If the angle is known and you need a side, forward mode gives the ratio, which you then multiply by the hypotenuse or adjacent side.<\/p>\n<p>For angles outside 0\u00b0\u2026360\u00b0, remember that all three functions are periodic: sine and cosine repeat every 360\u00b0 (2\u03c0 rad), and the tangent repeats every 180\u00b0 (\u03c0 rad). The calculator handles such inputs directly, so a 750\u00b0 angle or a \u221245\u00b0 angle produces correct values without any manual reduction.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate sin, cos and tan of any angle in degrees, radians or gradians \u2014 or enter a ratio and find the angle using arcsin, arccos or arctan.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[23],"class_list":["post-66832","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-geometry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66832","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=66832"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66832\/revisions"}],"predecessor-version":[{"id":67129,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66832\/revisions\/67129"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66832"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66832"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66832"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}