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Trigonometry Formula and Table

Trigonometry is an important branch of mathematics dealing with the study of relationship of length and angles. Usually, trigonometry is associated with right-angled triangles. A right angle is obtained when one of the angles is 90°. Trigonometry plays a vital role in many domains of mathematics. With the help of a trigonometric table, various geometric calculations can be easily worked out. This table consists of trigonometric functions and formulae based on specific angles.

The trigonometric ratios table provides great help to find the values of standard angles, namely 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°. This table is made up of trigonometric ratios such as sine, cosine, tangent, cosecant, secant and cotangent. The short forms of these ratios are sin, cos, tan, cosec, sec, and cot. The values contained in all these standard angles are necessary to solve the trigonometry problems. The values can easily be remembered with the help of some simple tricks.

This table is very helpful in different fields. It is mainly essential in navigation, oceanography, astronomy, science, and engineering. Interestingly, this method has been very effectively used in the pre-digital era, where there were no pocket calculators. Moreover, this table has also led to the development of the first mechanical computing devices. It also plays a key role in the foundation of the Fast Fourier Transform (FFT) algorithms.

Trigonometry Ratios Table

Angles (In Degrees) 30° 45° 60° 90° 180° 270° 360°
Angles (In Radians) π/6 π/4 π/3 π/2 π 3π/2
sin 0 1/2 1/√2 √3/2 1 0 -1 0
cos 1 √3/2 1/√2 1/2 0 -1 0 1
tan 0 1/√3 1 √3 0 0
cot √3 1 1/√3 0 0
cosec 2 √2 2/√3 1 -1
sec 1 2/√3 √2 2 -1 1

 

Remembering the ratio table can be very useful. It will be much easier to remember the table if one understands the trigonometric formulae.

Following are the formulae -

  • sin x = cos (90° - x)
  • cos x = sin (90° - x)
  • tan x = cot (90° - x)
  • cosec x = sec (90° - x)
  • sec x = cosec (90° - x)
  • cot x = tan (90° - x)
  • 1/sin x = cosec x
  • 1/cos x = sec x
  • 1/tan x = cot x

Given below are the formulae for 6 important trigonometric functions:

formulae

 

Trigonometric ratios are easily calculated with the help of these 6 formulae describing important trigonometric functions.

 

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