{"id":756,"date":"2020-12-08T08:37:16","date_gmt":"2020-12-08T08:37:16","guid":{"rendered":"https:\/\/pickedshares.com\/?p=756"},"modified":"2021-04-29T15:57:38","modified_gmt":"2021-04-29T15:57:38","slug":"important-angles-and-related-results-of-the-trigonometric-functions","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/important-angles-and-related-results-of-the-trigonometric-functions\/","title":{"rendered":"Important angles and related results of the trigonometric functions"},"content":{"rendered":"\n<p>The following table shows a selection of frequently used angles and the associated results of the trigonometric functions sine and cosine.<\/p>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n\\[ \\require{cancel} \\]\n\n<table>\n\n<tbody><tr>\n<td><b>\\[ [\\alpha]=rad \\]<\/b><\/td><td><b>\\[ [\\alpha]=\u00b0 \\]<\/b><\/td><td><b>\\[ \\sin \\alpha \\]<\/b><\/td><td><b>\\[ \\cos \\alpha \\]<\/b><\/td>\n<\/tr>\n\n\n<tr>\n<td>\\[ 0 \\]<\/td><td>\\[ 0\u00b0 \\]<\/td><td>\\[ 0 \\]<\/td><td>\\[ 1 \\]<\/td>\n<\/tr>\n<tr>\n<td>\\[ \\frac{\\pi}{6} \\]<\/td><td>\\[ 30\u00b0 \\]<\/td><td>\\[ \\frac{1}{2} \\]<\/td><td>\\[ \\frac{\\sqrt{3}}{2} \\]<\/td>\n<\/tr>\n<tr>\n<td>\\[ \\frac{\\pi}{4} \\]<\/td><td>\\[ 45\u00b0 \\]<\/td><td>\\[ \\frac{1}{\\sqrt{2}} \\]<\/td><td>\\[ \\frac{1}{\\sqrt{2}} \\]<\/td>\n<\/tr>\n<tr>\n<td>\\[ \\frac{\\pi}{3} \\]<\/td><td>\\[ 60\u00b0 \\]<\/td><td>\\[ \\frac{\\sqrt{3}}{2} \\]<\/td><td>\\[ \\frac{1}{2} \\]<\/td>\n<\/tr>\n<tr>\n<td>\\[ \\frac{\\pi}{2} \\]<\/td><td>\\[ 90\u00b0 \\]<\/td><td>\\[ 1 \\]<\/td><td>\\[ 0 \\]<\/td>\n<\/tr>\n<tr>\n<td>\\[ \\frac{2\\pi}{3} \\]<\/td><td>\\[ 120\u00b0 \\]<\/td><td>\\[ \\frac{\\sqrt{3}}{2} \\]<\/td><td>\\[ -\\frac{1}{2} \\]<\/td>\n<\/tr>\n<tr>\n<td>\\[ \\frac{3\\pi}{4} \\]<\/td><td>\\[ 135\u00b0 \\]<\/td><td>\\[ \\frac{1}{\\sqrt{2}} \\]<\/td><td>\\[ -\\frac{1}{\\sqrt{2}} \\]<\/td>\n<\/tr>\n<tr>\n<td>\\[ \\frac{5\\pi}{6} \\]<\/td><td>\\[ 150\u00b0 \\]<\/td><td>\\[ \\frac{1}{2} \\]<\/td><td>\\[ -\\frac{\\sqrt{3}}{2} \\]<\/td>\n<\/tr>\n<tr>\n<td>\\[ \\pi \\]<\/td><td>\\[ 180\u00b0 \\]<\/td><td>\\[ 0 \\]<\/td><td>\\[ -1 \\]<\/td>\n<\/tr>\n<\/tbody><\/table>\n\n\n\n<p>The shown values are typically used for simplified notation of mechanical equations. In addition, the table can be used for the conversion between \u00b0 and radiant.<\/p>\n\n\n\n<p><strong>Angle conversion from Degree (\u00b0) to Radiant<\/strong><\/p>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n<p>\\[ \\alpha_{Radiant} = \\frac{\\alpha_{Degree}}{180\u00b0} \\cdot \\pi \\]<\/p>\n\n\n\n<p><strong>Angle conversion from Radiant to Degree (\u00b0)<\/strong><\/p>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n<p>\\[ \\alpha_{Degree} = \\frac{\\alpha_{Radiant}}{\\pi} \\cdot 180\u00b0 \\]<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Important angles and related results of the trigonometric functions\" 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