Trigonometry Table 0 to 360 Values for Class 10
The Trigonometry table is known before the existence of calculators we are using in the present era. The Trigonometry Table aids in determining trigonometric ratio values for standard angles such as 0°, 30°, 45°, 60°, and 90°. The Trigonometry Table is useful in science, navigation, and engineering. The invention of the trigonometric table resulted in the creation of the first mechanical computer machines.
Trigonometry Ratio Table- sin cos tan Table
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 Trigonometry Table. Stay tuned and bookmark this page to get all the updates.
Trigonometry Ratio Table
Trigonometry Table Ratios is given below in the table.
| Trigonometry Ratio Table | ||||||||
| Angles (In Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |
| Angles (In Radians) | 0° | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |
| 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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Trigonometry Table Formula
Students must know the Trigonometry Table formulas because it made it easy for students to learn the Trigonometry Table. Even trigonometric ratios are depended upon the trigonometric formulas. To ease 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 tables. If students will already know the trigonometric formulas then learning Trigonometry Table will be easy for them.
Trigonometry Table 0-360 Value Formulas
Trigonometry Table (0-360) degree All formulas are given below.
- sin x = cos (90° – x)
- cot x = tan (90° – x)
- sec x = cosec (90° – x)
- cos x = sin (90° – x)
- tan x = cot (90° – x)
- cosec x = sec (90° – x)
- 1/sin x = cosec x
- 1/tan x = cot x
- 1/cos x = sec x
Trigonometry Table Questions for Class 10 and 12
Trigonometry Table (0°-360°) Preparation Trick for Class 10 and 12
We can easily create a Trigonometry Table by using the following steps-
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°, and 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) |
0° | 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) |
0° | 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) | 0° | 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) | 0° | 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) | 0° | 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) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |
| sec | 1 | 2/√3 | √2 | 2 | ∞ | -1 | ∞ | 1 |
Trigonometry Table 0 to 360 Degrees Values PDF
Trigonometry Table All values-PDF which are very useful for every exams.
Trigonometry Table Chart for Sin Cos tan 0-360 degrees
Trigonometry Table Chart is given below. take a close look to remember.
Trigonometry Table in Pi
Trigonometry Table in PI (π) check full table which is listed here.
| Angles (In pi) | 0° | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |
| 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 |
Trigonometric Table (0°-360°) Examples
Q.Find the Exact value of Sin 15 using trigonometry table values.
Answer- sin15 ° can be written as, sin(45° -30°)
sin15°= sin(45° -30°)= sin45° cos30°-cos45°sin30°,
[using formula sin(X-Y)=sinXcosY-cosXsinY]
or,sin15° = (1/√2 ×√3/2)- (1/2×1/√2) { using Trigonometery Table values }
sin15° = 1/√2 [(√3 -1)/2]
sin15° = (√3 -1)/2√2 (Answer)
Q. If θ =30°,prove that cos 2θ =cos²θ -sin² θ
Answer- θ =30°
R.H.S – cos²θ – sin² θ
= cos²30° – sin²30° = (1/2 )² – (√3/2 )² =3/4 – 1/4 = 1/2
L.H.S – cos 2θ
= cos 2 ( 30° )= Cos 60° = !/2
Hence, L.H.S =R.H.S [ Proved]
Q.Find the length of the ladder which is leaning against a wall with an angle of 60° and the foot of the ladder is 12.4 m away from the wall.
Answer- In the above question, the length of the base is 12.4 m. The elevation angle is 60°.
Now, let’s assume the length of the ladder is h m
Cos 60°= 12.4/ h
or,1/2 = 12.4/h
or, h = 2 ×12.4 = 24.8 m.
Hence, the length of the ladder is 24.8 m.
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Trigonometric Table 0°-360° Practice Questions
1. Using Trigonometry Table, find the value of [4/3 tan²60° + 3cos²30° – 2 sec²30° – 3/4cot² 60°]
2. Proves that {sin²30° +cos²30° =1} , using Trigonometry Table values.
3. Using Trigonometry Table, find the values of (a) tan (π/4) (b) sec(π/6) ( c) sec(π/3
4. If the length of the shadow of a tree is √3 times its real height, then calculate the angle of elevation of the sun.
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Trigonometric Table for Class 10 & 12 QNAs
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:
- Tan = Opposite/Adjacent
- Cot = 1/Tan = Adjacent/Opposite
- Sin = Opposite/Hypotenuse
- Sec = 1/Cos = Hypotenuse/Adjacent
- Cos = Adjacent/Hypotenuse
- 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 calculating 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 calculating the value of cosec on different angles?
Use this formula to calculate the value of cosec on different angles: cosec x = 1/sin x.
