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Trigonometry Table: Learning Tips and Tricks

trigonometry table

Trigonometry is the branch of mathematics that is used to determine the angle and distance of any object. In mathematics, it is mostly used for calculating the relations between the distance and angle of any triangle. The trigonometry table tells us the exact value of some standard angles for a right-angle triangle.

Here in this article, we have given a trigonometry table that is commonly known as the “trigonometric ratio table” or “trigonometric chart”. 

Before going for the trigonometry table, some basic terms you should know about trigonometry:

Six trigonometry functions/ratios: 

The six trigonometry functions or trigonometry ratios are:- sine, cosine, tangent, cotangent, secant, and cosecant.

Whereas the short form of these functions is:- sin, cos, tan, cot, sec, cosec. 

These trigonometry functions focus to find the relationship between angle and distance of a triangle, whereas the one angle of the triangle is right-angle or 90°.  

How to calculate the values for these trigonometry ratios for a right angle triangle are given below. 

Let’s consider there is a right-angle triangle with the sides of AB (BA), BC (CB), CA (AC). We have to calculate an angle “θ” with six trigonometry functions. Then the value of these six trigonometry ratios would be like:

trigonometry ratios

  • sin θ =Opposite/Hypotenuse = BC/AC
  • cos θ = Adjacent/Hypotenuse = AB/AC
  • tan θ = Opposite/Adjacent = BC/AB
  • cot θ = 1/(tan θ) = Adjacent/Opposite = AB/BC
  • sec θ = 1/(cos θ) =  Hypotenuse/Adjacent = AC/AB
  • cosec θ = 1/(sin θ) = Hypotenuse/Opposite = AC/BC

Trigonometry table for standard angle 

Here is the given trigonometry table for standard angles 0°, 30°, 45°, 60°, 90°. You can also call it “sin cos tan table”, “sin cos tan chart”, “sin cos tan value table”, “trigonometric values table” or “trigonometry formula table”. The infinity ∞ is not defined value (ND). 

Angles ⇒ 0° 30° 45° 60° 90°
sin 0 1/2 1/√2 √3/2 1
cos 1 √3/2 1/√2 1/2 0
tan 0 1/√3 1 √3 ∞ (ND)
cot ∞ (ND) √3 1 1/√3 0
sec 1 2/√3 √2 2 ∞ (ND)
cosec ∞ (ND) 2 √2 2/√3 1

Learning tips and tricks for trigonometry table

Believe me, this trigonometry table is very easy to learn. We have given some tips and tricks to learn trigonometry ration tables. All you have to do ‘remember the values for sine angle’ and it would help to generate all values of other trigonometric ratios just in your mind. 

Let’s suppose you remember the sin values for angle 0° to 90°.

Trick for cos:

Now for cos 0° to 90° values, reverse the sin values from 90° to 0°. It means:

  • cos 0° = sin 90°,
  • cos 30° = sin 60°,
  • cos 45° = sin 45°,
  • cos 60° = sin 30°,
  • cos 90° = sin 0°. 

Trick for tan

Now for tan 0° to 90° values, divide sin values with cos values. It means:

  • tan 0° = sin 0°/cos 0° = 0/1 = 0,
  • tan 30° = sin 30/cos 30 = 1/√3
  • tan 45° = sin 45/cos 45 = 1
  • tan 60° = sin 60/cos 60 = √3
  • tan 90° = sing 90/com 90 = ∞

Trick for cot

For calculating the value of cot 0° to 90°, all we have to reverse the tan values. It means:

  • cot 0° = 1/tan 0° = ∞
  • cot 30° = 1/tan 30° = √3
  • (cot 45, cot 60, cot 90… practice it…)

Trick for sec

For calculating the value of sec 0° to 90°, all we have to reverse the cos values. It means:

  • sec 0° = 1/cos 0° = 1
  • sec 30° = 1/cos 30° = 2/√3
  • (sec 45, sec 60, sec 90… practice it…)

Trick for cosec

For calculating the value of cosec 0° to 90°, all we have to reverse the sin values. It means:

  • cosec 0° = 1/sin 0° = ∞
  • cosec 30° = 1/sin 30° = 2
  • (cosec 45, cosec 60, cosec 90… practice it…)

How I had learned the trigonometry value table?

For sharing my experience to learn the trigonometry table, I had to do some practice and used a trick. I did not use these tricks. Only cot, sec, cosec tricks I had used. and I had remembered three trigonometry ratios angle values: sin, cos, tan. After remembering these three I used to reverse in my mind. You can also practice this, it would be easy. But do not forget to learn or remember the first three. 

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