Trigonometric Table: Formula, Value, Chart, PDF

Trigonometric Table Value from 0 to 180 for Class 10 and 11

The trigonometric table is known before the existence of calculators we are using in the present era. The trigonometric table aids in determining trigonometric ratio values for standard angles such as 0°, 30°, 45°, 60°, and 90°.  The trigonometric table is useful in science, navigation, and engineering. The invention of the trigonometric table resulted in the creation of the first mechanical computer machines. Trigonometric ratios are included in the trigonometric table: sine, cosine, tangent, cosecant, secant, and cotangent. These ratios are abbreviated as sin, cos, tan, cosec, sec, and cot.  The Fast Fourier Transform algorithms are another notable application of trigonometric tables. In solving trigonometry issues, the values of trigonometric ratios of standard angles in a trigonometry table are useful. In this article, we will discuss the tricks to create the trigonometric table. Stay tuned and bookmark this page to get all the updates. 

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

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Trigonometric Table Formula

Students must know the trigonometry formulas because it made it easy for students to learn the trigonometric table. Even trigonometric ratios are depended upon the trigonometric formulas. To ease of students below we have given the trigonometric formulas. The students are advised to learn trigonometry formulas first before jumping on the steps to learn trigonometric table. If students will already know the trigonometric formulas then learning trigonometric tables will be easy for them. 

Basic Trigonometric Formulas 

  1. sin x = cos (90° – x)
  2. cot x = tan (90° – x)
  3. sec x = cosec (90° – x)
  4. cos x = sin (90° – x)
  5. tan x = cot (90° – x)
  6. cosec x = sec (90° – x)
  7. 1/sin x = cosec x
  8. 1/tan x = cot x
  9. 1/cos x = sec x

Step 1: Make a table with the top row listing the angles such as 0°, 30°, 45°, 60°, 90°, and the first column containing the trigonometric functions such as sin, , cosec, cos, tan, cot, sec. 

Step 2: calculating the value of sin for different angles: In ascending order, write the angles 0°, 30°, 45°, 60°, 90° and assign them the numbers 0, 1, 2, 3, 4 according to the order. As a result, 0 will be assigned to 0°; 1 will be assigned to 30°; 2 will be assigned to 45°; 3 will be assigned to  60°; 4 will be assigned to 90°. Next, divide the values by four and square root the total value. 

 0° ⟶ √(0/4) = 0

30° ⟶ √(1 /4) = 1/2 

45° ⟶ √(2/4) = 1/ √2

60° ⟶√(3/4) = √3/2

90° ⟶ √(4/4) = 1

This offers the sine values for these 5 angles i.e. 0°, 30°, 45°, 60°, 90°. Now for the last three angles we will use the formula given below:

sin (180° − x) = sin x

sin (180° + x) = -sin x

sin (360° − x) = -sin x

Calculate the values of 180º, 270º, 360º   

sin (180° − 0º) = sin 0º 

Here we are taking x = 0 because we have to find the value of Sin 180º. Thus, putting x = 0º  is satisfying the formula. 

sin (180° + 90º) = -sin 90º

Here we are taking x = 90º because we have to find the value of Sin 270º. Thus, putting x = 90º  is satisfying the formula.  

sin (360° − 0º) = -sin 0º

Here we are taking x = 0º because we have to find the value of Sin 360º. Thus, putting x = 0º  is satisfying the formula.  

 

Angles

(in Degrees)

30° 45° 60° 90° 180° 270° 360°
sin 0 1/2 1/√2 √3/2 1 0 -1 0

 

Step 3: To find the value of cos, use the formula sin (90° – x) = cos x. Use this formula to calculate cos x for all the angles. 

Example: 

for value of X =  0°

Cos 0° = sin (90° – 0°) = sin 90°

for value of X =  30°

cos 30° = sin (90° – 30°) = sin 60°.

for value of X =  45°

Cos 45° = sin (90° – 45°) = sin 45°

for value of X =  60°

cos 60° = sin (90° – 60°) = sin 30°

for value of X =  90°

cos 90° = sin (90° – 90°) = sin 0°

for value of X =  180°

cos 180° = sin (90° – 180°) = -sin 90°

for value of X =  270°

cos 270° = sin (90° – 270°) = -sin 180°

for value of X =  360°

cos 360° = sin (90° – 360°) = -sin 270°

Angles

(in Degrees)

30° 45° 60° 90° 180° 270° 360°
cos 1 √3/2 1/√2 1/2 0 -1 0 1

 

Step 4: Calculate the value of tan for all the angles. Use the formula given below: 

 tan x = sin x/cos x

Calculate the value of tan by putting all the angles in the formula given above.

Angles (In Degrees) 30° 45° 60° 90° 180° 270° 360°
tan 0 1/√3 1 √3 0 0

 

Step 5: Calculate the value of the cot for all the angles. Use the formula given below: 

cot x = 1/tan x

Calculate the value of the cot by putting all the angles in the formula given above.

Angles (In Degrees) 30° 45° 60° 90° 180° 270° 360°
cot √3 1 1/√3 0 0

 

Step 6: Calculate the value of cosec for all the angles. Use the formula given below: 

cosec x = 1/sin x

Calculate the value of cosec by putting all the angles in the formula given above.

Angles (In Degrees) 30° 45° 60° 90° 180° 270° 360°
cosec 2 √2 2/√3 1 -1

 

Step 7: Calculate the value of sec for all the angles. Use the formula given below: 

sec x = 1/cos x

Calculate the value of sec by putting all the angles in the formula given above.

Angles (In Degrees) 30° 45° 60° 90° 180° 270° 360°
sec 1 2/√3 √2 2 -1 1

Trigonometric Table PDF

Trigonometric Table Chart

Trigonometric Table Chart

Trigonometric Table in terms of Pi

Angles (In pi) 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

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FAQs on Trigonometric Table Value

Q. What is the value of Sin 0°?

The value of Sin 0° is Zero.

Q. How to find the value of trigonometric functions on different angles?

All trigonometric functions are related to the triangle’s sides, and their values can be easily found using the following relationships:

  1. Tan = Opposite/Adjacent
  2. Cot = 1/Tan = Adjacent/Opposite
  3. Sin = Opposite/Hypotenuse
  4. Sec = 1/Cos = Hypotenuse/Adjacent
  5. Cos = Adjacent/Hypotenuse
  6. Cosec = 1/Sin = Hypotenuse/Opposite

Q. What is the value of Cos  0°?

The value of Cos 0° is 1.

Q. What is the trick to calculate the value of tan on different angles?

Use this formula to calculate the value of tan on different angles:  tan x = sin x/cos x

Q. What is the trick to calculate the value of cosec on different angles?

Use this formula to calculate the value of cosec on different angles: cosec x = 1/sin x.

 

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