How to Create a Trig 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 sin function.
For finding the values of the sin function, divide 0, 1, 2, 3, and 4 by 4 and take under the root of each value, respectively as,
For, the value of sin 0° = √(0/4) = 0
Similarly,
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 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 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 |
Trigonometry Table | Trigonometric Ratios and Formulas
Trigonometry Table is a standard table that helps us to find the values of trigonometric ratios for standard angles such as 0°, 30°, 45°, 60°, and 90°. It consists of all six trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent.
Let’s learn about the trigonometry table in detail.
Table of Content
- Trigonometry Table
- Trigonometric Functions Table
- Trick To Learn Trigonometric Ratios
- How to Memorize Trigonometric Table
- How to Create a Trig Table
- Trigonometric Formulas
- Trigonometric Identities Table
- Trigonometric Table Examples
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