Trigonometry Table | Trigonometric Ratios and Formulas

The 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.

The most common values of trigonometric ratios are given in the table below:

Read More about the Trick to Remember the Trigonometry Table.

Trigonometric Functions Table

Trigonometry has 6 basic trigonometric functions they are sine, cosine, tangent, cosecant, secant, and cotangent. Now let’s look into the trigonometric functions.

For, any right-angle triangle with perpendicular(P), Base(B), and Hypotenuse(H) the six trigonometric functions are as follows,

Also, Read about Trigonometric Ratios.

Learn the Trick to Remember Trigonometric Ratios- [SOHCAHTOA]
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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, 

• sin 30° = √(1/4) = 1/2
• sin 45° = √(2/4) = 1/√2
• sin 60° = √(3/4) = √3/2
• sin 90° = √(4/4) = 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

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

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,

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,

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,

In this way, we can create the following trigonometric ratios table:

Next Article: Trigonometry Formulas.