{"id":5045,"date":"2019-01-27T21:45:32","date_gmt":"2019-01-27T16:15:32","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=5045"},"modified":"2023-04-02T18:30:53","modified_gmt":"2023-04-02T13:00:53","slug":"trigonometric-ratios-table","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/trigonometric-ratios-table\/","title":{"rendered":"How to easily remember trigonometric ratios table (0-90)"},"content":{"rendered":"\n

Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between their sides and angles. One of the fundamental concepts in trigonometry is trigonometric ratios, which are ratios of the sides of a right triangle to its angles. There are six trigonometric ratios – sine, cosine, tangent, cosecant, secant, and cotangent – that are used to solve problems related to angles, distances, and heights. In this article, we will discuss a trigonometric ratios table that can help students understand these ratios easily.<\/p>\n\n\n\n

Trigonometric ratios table<\/h2>\n\n\n\n

Trigonometric ratios table for standard angles (0-90) is given as<\/p>\n\n\n\n

\"trigonometric<\/a><\/figure>\n\n\n\n

Students often find it difficult to remember and use it trigonometric equations, questions and problems<\/p>\n\n\n\n

There is one easy way to remember these trigonometric ratios table.Lets check it out<\/p>\n\n\n\n

1.For sin ratios for 0,30 ,45 ,60 and 90, we can remember them as by taking square root of the fraction of 0\/4,1\/4,2\/4,3\/4,4\/4<\/p>\n\n\n\n

$sin 0 = \\sqrt { \\frac {0}{4}} = 0$<\/p>\n\n\n\n

$sin 30 = \\sqrt {\\frac  {1}{4}} = 1\/2$<\/p>\n\n\n\n

$sin 45 = \\sqrt {\\frac {2}{4}} = \\frac {1}{ \\sqrt {2}}$<\/p>\n\n\n\n

$sin 60 = \\sqrt { \\frac {3}{4}} = \\frac {\\sqrt {3}}{2}$<\/p>\n\n\n\n

$sin 90 = \\sqrt {\\frac {4}{4}} =1$<\/p>\n\n\n\n

\"How<\/a><\/figure>\n\n\n\n

2.for cos ratios for 0,30 ,45 ,60 and 90, we can remember them as opposite order from sin 90 to 0<\/p>\n\n\n\n

$cos 0 = sin 90 =1$<\/p>\n\n\n\n

$cos 30 =sin 60 = \\frac {\\sqrt {3}}{2}$<\/p>\n\n\n\n

$cos 45= sin45 =\\frac {1}{ \\sqrt {2}}$<\/p>\n\n\n\n

$cos 60 =sin 30 = 1\/2 $<\/p>\n\n\n\n

$cos 90 =sin 0 =0$<\/p>\n\n\n\n

\"trigonometry<\/a><\/figure>\n\n\n\n

3.for tan ratios for 0,30 ,45 ,60 and 90, we can remember them as<\/p>\n\n\n\n

$tan x = \\frac {sin x}{cos x}$<\/p>\n\n\n\n

$tan 0 = 0\/1 =0$<\/p>\n\n\n\n

$tan 30 =  \\frac {sin 30}{cos 30}= \\frac {1}{ \\sqrt {3}}$<\/p>\n\n\n\n

$tan 45 =  \\frac {sin 45}{cos 45}= 1$<\/p>\n\n\n\n

$tan 60 =  \\frac {sin 60}{cos 60}= \\sqrt {3}$<\/p>\n\n\n\n

$tan 90 = \\frac {sin 90}{cos 90}= 1\/0 $ .This is undefined<\/p>\n\n\n\n

\"standard<\/a><\/figure>\n\n\n\n

(4) For cosec ratios for 0,30 ,45 ,60 and 90, we can remember them as<\/p>\n\n\n\n

$cosec A = \\frac {1}{sinA}$<\/p>\n\n\n\n

$ cosec 0 = 1\/0$ .This is undefined<\/p>\n\n\n\n

$cosec 30 = \\frac {1}{sin30} =2$<\/p>\n\n\n\n

$cosec 45 = \\frac {1}{sin45} =\\sqrt {2}$<\/p>\n\n\n\n

$cosec 60 = \\frac {1}{sin60} =\\frac {2} {\\sqrt {3}}$<\/p>\n\n\n\n

$cosec 90 = \\frac {1}{sin90} =1$<\/p>\n\n\n\n

\"How<\/a><\/figure>\n\n\n\n

5.for sec ratios for 0,30 ,45 ,60 and 90, we can remember them as<\/p>\n\n\n\n

$sec A = \\frac {1}{cosA}$<\/p>\n\n\n\n

$ sec 0 = 1$ .<\/p>\n\n\n\n

$sec 30 = \\frac {1}{cos30} =\\frac {2} {\\sqrt {3}}$<\/p>\n\n\n\n

$cosec 45 = \\frac {1}{cos45} =\\sqrt {2}$<\/p>\n\n\n\n

$cosec 30 = \\frac {1}{sin60} =2$<\/p>\n\n\n\n

$cosec 90 = \\frac {1}{cos90} =1\/0$. This is undefined<\/p>\n\n\n\n

\"sin<\/a><\/figure>\n\n\n\n

6.for cot ratios for 0,30 ,45 ,60 and 90, we can remember them as<\/p>\n\n\n\n

$cot x = \\frac {cos x}{sin x}$<\/p>\n\n\n\n

$cot 0 = 1\/0 $ This is undefined<\/p>\n\n\n\n

$cot 30 =  \\sqrt {3}$<\/p>\n\n\n\n

$cot 45 =  1$<\/p>\n\n\n\n

$tan 60 =  \\frac {1}{ \\sqrt {3}}$<\/p>\n\n\n\n

$cot 90 =\u00a0\\frac {cos 90}{sin 90}= 0 $ .<\/p>\n\n\n\n

Benefits of Trigonometric Ratios Table:<\/h2>\n\n\n\n