How to Remember the Trigonometric Table

Step-by-Step Guide

1. 1

   Step 1: Create a table.

   In the first row, write down the trigonometric ratios (sin, cos, tan, cot).
   
   In the first column, write down the angles (0°, 30°, 45°, 60°, 90°).
   
   Leave other entries blank.
2. 2

   Step 2: Fill in the sine column.

   We will fill in the blank entries in the sin column using the expression √x/2.
   
   Once the sine column is filled, we'll be able to fill all other columns effortlessly! For the 1st entry in the sine column (that is, sin 0°), set x = 0 and plug it in the expression √x/2.
   
   Thus, sin 0° = √0/2 = 0/2 = 0 For the 2nd entry in the sine column (that is, sin 30°), set x = 1 and plug it in the expression √x/2.
   
   Thus, sin 30° = √1/2 = 1/2 For the 3rd entry in the sine column (that is, sin 45°), set x = 2 and plug it in the expression √x/2.
   
   Thus, sin 45° = √2/2 = 1/√2 For the 4th entry in the sine column (that is, sin 60°), set x = 3 and plug it in the expression √x/2.
   
   Thus, sin 60° = √3/2.
   
   For the 5th entry in the sin column (that is, sin 90°), set x = 4 and plug it in the expression √x/2.
   
   Thus, sin 90° = √4/2 = 2/2 =
   1. , Simply copy the entries in the sine column in reverse order into the cosine column.
   
   This is valid because sin x° = cos (90-x)° for any x. , We know that tan = sin / cos.
   
   So, for every angle take its sin value and divide it by the cos value to get the corresponding tan value.
   
   For example, tan 30° = sin 30° / cos 30° = (√1/2) / (√3/2) = 1/√3 , Simply copy the entries in tangent column in reverse order into the cot column.
   
   This is valid because tan x° = sin x° / cos x° = cos (90-x)° / sin (90-x)° = cot (90-x)° for any x.
3. 3

   Step 3: Fill in the cosine column.

4. 4

   Step 4: Fill in the tangent column.

5. 5

   Step 5: Fill in the cotangent column.

Detailed Guide

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