Trigonometry Table Formula: Trigonometry is a branch of mathematics that focuses on the relationship between angles and sides of triangles. The trigonometry table is also known as a trig table or an angle table. It is one of the important tools in trigonometry. The trigonometry table serves as a reference guide, providing the values of trigonometry functions for different angles.
Sine, cosine, and tangent are the three basic trigonometric functions that define the ratios between the sides of a right triangle. Since these functions are presented in a systematic format in the trigonometry table, users can quickly obtain the values without performing complex calculations. It typically covers angles from 0 to 90 degrees, as these angles correspond to the primary quadrants of the unit circle.
In the table, each row signifies a distinct angle, with columns presenting the angle in degrees, along with its sine, cosine, and tangent values. This article elucidates efficient methods to grasp trigonometry tables for classes 10, 11, and 12, along with additional insights.
Trigonometry Table:
The following is the trigonometry table showing the values of common trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for angles in degrees.
Degrees
( 0 ) |
Sine
(sin) |
Cosine
(cos) |
Tangent
(tan) |
Cosecant
(csc) |
Secant
(sec) |
Cotangent
(cot) |
00 | 0 | 1 | 0 | ∞ | 1 | ∞ |
30^0 | 1/2 | √3/2 | 1/√3 | 2 | 2/√3 | √3 |
45^0 | 1/√2 | 1/√2 | 1 | √2 | √2 | 1 |
60^0 | √3/2 | 1/2 | √3 | 2/√3 | 2 | 1/√3 |
90^0 | 1 | 0 | ∞ | 1 | ∞ | 0 |
180^0 | 0 | -1 | 0 | ∞ | -1 | ∞ |
270^0 | -1 | 0 | ∞ | -1 | ∞ | 0 |
360^0 | 0 | 1 | 0 | ∞ | 1 | ∞ |
In this table 1/√2 can also be written as √2/2 and 1/√3 can also be written as √3/3 ( by rationalizing the denominators)
Formulas For Trigonometry Table:
The following are the Trigonometry Table (0 to 360 degrees) formulas.
- sin x = cos ( 90^0 – x )
- cot x = tan ( 90^0 – x )
- sec x = cosec ( 90^0 – x )
- cos x = sin ( 90^0 – x )
- tan x = cot ( 90^0 – x )
- cosec x = sec ( 90^0 – x )
- cosec x = 1/sin x
- cot x = 1/tan x
- sec x = 1/cos x
How To Learn Trigonometry Table For Class 10, Class 11 & 12?
The trigonometry table may appear difficult at first, but it is simple to understand if you know the sine values for the eight standard angles. There are a few formulas that must be followed before generating the table. The formulas are mentioned below.
- Tan x = sin x / cos x
- Cosec x = 1 / sin x
- Sec x = 1 / cos x
- Cot x = 1 / tan x or cos x / sin x.
Here are the steps for making a trigonometric table that you can remember.
Step 1: Create a table with the trigonometry functions sin, cosec, cos, tan, cot, and sec in the first column and the angles 0^0, 30^0, 45^0, 60^0, 90^0, 180^0, 270^0, and 360^0 in the top row.
Step 2: Calculating the value of sin x:
Angles 0^0, 30^0, 45^0, 60^0, and 90^0 should be written in ascending order. For each of these angles, sin has the values 0, 1/2, 1/√2, √3/2, and 1 respectively. This information provides the sine values for these five angles. Now utilize the following formulas for the final three.
sin (180^0 – x) = sin x
-sin x = sin (180^0 + x)
sin (360^0 – x) = -sin x
This means,
Sin 180^0 = sin (180^0 – 0^0) = sin 0^0 = 0, here we are taking x = 0 because we need to determine the value of sin 180^0. Thus putting x = 0^0 fulfils the requirements of the formula.
Sin 270^0 = sin (180^0 + 90^0) = -sin 90^0 = -1, here we are using x = 900 in this case because we need to calculate the value of sin 270^0. As a result, x = 90^0 fulfills the requirements of the formula.
Angles
(in Degree) |
0^0 | 30^0 | 45^0 | 60^0 | 90^0 | 180^0 | 270^0 | 360^0 |
Sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | -1 | 0 |
Sin 360^0 = sin (360^0 – 0^0) = -sin 0^0 = 0, here we are using x = 00 in this case because we need to calculate the value of sin 3600. As a result, x = 00 fulfils the requirements of the formula.
3rd Step: Calculate the values of cos x:
Cos x = sin ( 90^0 – x ). To calculate cos x values, use this formula.
Cos 0^0 = sin ( 90^0 – 0^0 ) = sin 90^0 = 1, where x = 0^0
Cos 30^0 = sin ( 90^0 – 30^0 ) = sin 60^0 = √3/2, where x = 30^0
where x = 45^0, Cos 45^0 = sin ( 90^0 – 45^0 ) = sin 45^0 = 1/√2.
Cos 60^0 = sin ( 90^0 – 60^0 ) = sin 30^0 = 1/2, where x = 60^0
Cos 90^0 = sin ( 90^0 – 90^0 ) = sin 0^0 = 0, where x = 90^0
where x = 180^0, Cos 180^0 = sin ( 90^0 – 180^0 ) = -sin 90^0 = -1
Cos 270^0 = sin ( 90^0 – 270^0 ) = -sin 180^0 = 0, where x = 270^0
Cos 360^0 = sin ( 90^0 – 360^0 ) = -sin 270^0 = 1, where x = 360^0
Angles
(in Degree) |
0^0 | 30^0 | 45^0 | 60^0 | 90^0 | 180^0 | 270^0 | 360^0 |
cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | -1 | 0 | 1 |
4th Step: Determining the values of tan x:
Tan x = sin x / cos x. Hence, we need to put all the angles in the given formula and calculate the value of tan. For example, tan 0^0 = sin 0^0 / cos 0^0 = 0/1 = 0. Similarly, tan 30^0 = sin 30^0 / cos 30^0 = ( 1/2 )/(√3/2) = 1/√3. Using this, you can easily determine the values of the tan function as,
Angles
(in Degree) |
0^0 | 30^0 | 45^0 | 60^0 | 90^0 | 180^0 | 270^0 | 360^0 |
tan | 0 | 1/√3 | 1 | √3 | ∞ | 0 | ∞ | 0 |
5th Step: Calculating the values of cot x:
cot x = 1 / tan x. Hence, we need to put all the angles in the given formula and calculate the value of the cot. By using this formula, you can easily determine the values of the cot function as,
Angles
(in Degree) |
0^0 | 30^0 | 45^0 | 60^0 | 90^0 | 180^0 | 270^0 | 360^0 |
cot | ∞ | √3 | 1 | 1/√3 | 0 | ∞ | 0 | ∞ |
6th Step: Calculating the values of cosec x:
cosec x = 1 / sin x. Hence, we need to put all the angles in the given formula and calculate the value of cosec. By using this formula, you can easily determine the values of the cosec function as,
Angles
(in Degree) |
0^0 | 30^0 | 45^0 | 60^0 | 90^0 | 180^0 | 270^0 | 360^0 |
cosec | ∞ | 2 | √2 | 2/√3 | 1 | ∞ | -1 | ∞ |
7th Step: Finding the values of sec x:
sec x = 1 / cos x. Hence, we need to put all the angles in the given formula and calculate the value of sec. By using this formula, you can easily determine the values of the sec function as follows,
Angles
(in Degree) |
0^0 | 30^0 | 45^0 | 60^0 | 90^0 | 180^0 | 270^0 | 360^0 |
sec | 1 | 2/√3 | √2 | 2 | ∞ | -1 | ∞ | 1 |
Trigonometry Pi Table:
The Trigonometry table is an essential reference tool for anyone studying or working with trigonometry. The table simplifies trigonometry calculations, enhances problem-solving capabilities, and aids in the exploration of the relationship between angles and trigonometry functions by providing re-calculated values of sin, cosine, tan, cot, cosec, and sec for different angles.