# Trigonometry Table

## Trigonometric Formula, Ratio and Angle Table

Trigonometry as a branch in Mathematics concerns itself with the study of length, angles and their relationships in a triangle. It is most often associated with the right-angled triangle, with one of the angles equal to 90 degrees always.

The trigonometric table is made up of the following of trigonometric ratios that are interrelated to each other – sine, cosine, tangent, cosecant, secant, cotangent. These ratios, in short, can be written as sin, cos, tan, cosec, sec and cot.

sin = perpendicular / hypotenuse
cos = base / hypotenuse
tan = perpendicular / base
cosec = hypotenuse / perpendicular

The applications of Trigonometry in other associated scientific and mathematical fields is enormous with the distances on earth as well as in space being estimated in the ancient world with careful use and application of Trigonometry.

The calculations can easily be figured out by memorizing a table of functions most commonly known as the Trigonometric Table. This find use in several areas. Some of them include navigation science, geography, engineering, geometry etc. The trigonometric table was the reason for most digital development to take place at this rate today as the first mechanical computing devices found application through careful use of trigonometry.

The Trigonometric ratios table gives us the values of standard trigonometric angles such as 0°, 30°, 45°, 60°, and 90°. These values hold increased precedence as compared to others as the most important problems employ these ratios. It is therefore very important to know and remember the ratios of these standard angles.

Memorizing the Trigonometric Table easily

Memorizing the trigonometry table will be useful as it finds many applications, and there are many methods to remember the table. Knowing the Trigonometric Formulae automatically will lead to figuring out the table and the values. The Trigonometry ratio table is depended upon the trigonometry formulas in the same way all the functions of trigonometry are interlinked with each other.

Before attempting to begin, it is better to try and remember these values, and know the following trigonometric formulae.

sin x = cos (90∘−x)
cos x = sin (90∘−x)
tan x = cot (90∘−x)
cot x = tan (90∘−x)
sec x = cot (90∘−x)
cot x = sec (90∘−x)
1 / sin x = 1 / cos x = sin x
1 / cos x= sec x
1 / sec x= cos x
1 / tan x= cot x
1 / cot x= tan x

Steps to Create Trigonometry Table:

Step 1: Draw a tabular column with the required angles such as 0, 30, 45, 60, 90, in the top row and all 6 trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent in first column.

Step 2: Find the sine value of the required angle
To determine the value of sin we divide all the values by 4 and then take the square root.

Step 3: Find the cosine value of the required angle
The cos values are tabularly opposite to that of sin angles.
This means that whichever values of sin (0 - x) degree is the same as the value of cos (90 - x) degree. To find the value of cos divide by 4 in the opposite order of sin and take the square root.

Step 4: Find the tangent value of the required angle
The tangent is equal to sine divided by cosine. tan x=sinx. cos x

Step 5: Determine the value of cot.
The value of cot can be determined by all inverse values of tan.
So, for every value, the cot value is 1 / tan. As cot x = cos x. sin x

Step 6: Find the cosecant value of the required angle
The value of cosec on any angle is the inverse of sin on that particular angle

Step 7: Determine the value of sec.
The value of sec on any angle is the inverse of cos of that particular angle.