A trigonometry table is a table that lists the values of trigonometric functions such as sine (sin), cosine (cos), and tangent (tan) for different angles, usually in degrees or radians.
This table is used to quickly find the values of these functions for solving problems in mathematics, physics, and engineering.
How to Create a Trigonometry Table
Study the following steps to create the trigonometric table for standard angles.
Step 1: Create the Table
Create a table and list all the angles, such as 0°, 30°, 45°, 60°, and 90°, in the top row. Enter all trigonometric functions sin, cos, tan, cosec, sec, and cot in the first column.
Step 2: Evaluate the value for all the angles of the sine function.
For finding the values of the sin function, divide 0, 1, 2, 3, and 4 by 4 and take under root of each value, respectively, as,
For the value of sin 0° = √(0/4) = 0. Similarly,Â
- sin 30° = √(1/4) = 1/2
- sin 45° = √(2/4) = 1/√2
- sin 60° = √(3/4) = √3/2
- sin 90° = √(4/4) = 1
| sin 0° | sin 30° | sin 45° | sin 60° | sin 90° |
|---|---|---|---|---|
| 0 | 1/2 | 1/√2 | √3/2 | 1 |
Step 3: Evaluate the value for all the angles of the cos function
The value of the cos function is the opposite of the value of the sin function, i.e., cos 0° = sin 90°, cos 30° = sin 60°, and cos 45° = sin 45°, so
| cos 0° | cos 30° | cos 45° | cos 60° | cos 90° |
|---|---|---|---|---|
| 1 | √3/2 | 1/√2 | 1/2 | 0 |
Step 4: Evaluate the value for all the angles of the tan function
The value of the tan function is equal to the sin function divided by the cos function, i.e., tan x = sin x / cos x. The value of all the angles in the tan function is calculated as,
tan 0°= sin 0° / cos 0° = 0/1 = 0, similarly
| tan 0° | tan 30° | tan 45° | tan 60° | tan 90° |
|---|---|---|---|---|
| 0 | 1/√3 |   1 |   √3 | Not Defined |
Step 5: Evaluate the value for all the angles of the cosec function
The value of the cosec function is equal to the reciprocal of the sin function. The value of cosec 0° is obtained by taking the reciprocal of sin 0°
cosec 0° = 1 / sin 0° = 1 / 0 = Not Defined. Similarly,
| cosec 0° | cosec 30° | cosec 45° | cosec 60° | cosec 90° |
|---|---|---|---|---|
| Not Defined | 2 | √2 | 2/√3 | 1 |
Step 6: Evaluate the value for all the angles of the sec function
The value of the sec function is equal to the reciprocal of the cos function. The value of sec 0° is obtained by taking the reciprocal of cos 0°
sec 0° = 1 / cos 0° = 1 / 1 = 1. Similarly,
| sec 0° | sec 30° | sec 45° | sec 60° | sec 90° |
|---|---|---|---|---|
| 1 | 2/√3 | √2 | 2 | Not Defined |
Step 7: Evaluate the value for all the angles of the cot function
The value of the cot function is equal to the reciprocal of the tan function. The value of cot 0° is obtained by taking the reciprocal of tan 0°
cot 0° = 1 /tan 0° = 1 / 0 = Not defined. Similarly,
| cot 0° | cot 30° | cot 45° | cot 60° | cot 90° |
|---|---|---|---|---|
| Not Defined | √3 | 1 | 1/√3 | 0 |
In this way, we can create the following trigonometric ratios table:
Degrees and Radians Trigonometric Table | |||||||
|---|---|---|---|---|---|---|---|
| Angle (in degrees) | Angle (in radians) | Sin | Cos | Tan | Cosec | Sec | Cot |
| 0° | 0 | 0 | 1 | 0 | Undefined | 1 | Undefined |
| 30° | π/6 | 1/2 | √3/2 | 1/√3 | 2 | 2/√3 | √3 |
| 45° | π/4 | √2/2 | √2/2 | 1 | √2 | √2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 | 2/√3 | 2 | 1/√3 |
| 90° | π/2 | 1 | 0 | Undefined | 1 | Undefined | 0 |
Trick to Memorize Trigonometric Table
Trigonometry Table is quite easy to remember if you know all the trigonometry formulas. There is also a trick called the one-hand trick to memorize the trigonometry table.
- Hold up your right hand with all five fingers extended. Each finger will represent a specific angle, starting from the pinky (representing 0°) and moving towards the thumb (representing 90°) similar to the following figure.
- Â Step 1: In the figure above, for the sine table, count the fingers on the left side for the standard angle.
- Â Step 2: Divide the number calculate in the 1st step by 4
- Â Step 3: Find the Square root of the value calculated in Step 2.
Result: This will result in the values of sine trigonometric ratios.
To find cosine and tangent values we can use the following:
- The cosine values mirror the sine values but in reverse order.
- Tangent is the ratio of sine to cosine, so you can use the sine and cosine values to get the tangent values.
Note:Â Cosec, Cot and Sec are reciprocal of Sin, Tan and Cos respectively, thus we can calculate those values using reciprocal of the founded values.
