Trigonometry Table: Trigonometry Table comprises the values of various trigonometric ratios for standard angles, like 0°, 30°, 45°, 60°, and 90°. Sine, cosine, tangent, cotangent, secant, and cosecant are the six trigonometric ratios. The trigonometry table showcases the values of these trigonometric ratios for different angles. Knowing these values can make it easier to solve various trigonometric problems.
Trigonometry is the branch of mathematics that deals with the relationship between the sides and angles of a triangle. Usually, it is associated with right-angled triangles, wherein one of the three angles of a triangle is a right angle. This helps in simplifying calculations and solving a wide variety of geometrical problems.
For example, if you are on the terrace of a tall building of known height and there is a post box on the other side of the road, across the building, your position on top of the building (Point A), the foot of the building (Point B), and the location of the post box (Point C) form a right-angled triangle. You can easily calculate the width of the road using trigonometry. There are various applications of Trigonometry in the field of construction, flight engineering, criminology, marine biology, and engineering, etc.
This article will provide you with the trigonometry ratio table and tricks to memorize the trigonometry table formula so that you can directly use them to solve problems.
Trigonometry Table: Trigonometric Formula, Ratio And Angle | Trigonometry Table Formula
As mentioned above, the trigonometry table contains the values of trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) of standard angles. Let us have a look at the trigonometric ratios table:
Angles in Degrees | 0° | 30° | 45° | 60° | 90° |
Angles in Radians | 0° | π/6 | π/4 | π/3 | π/2 |
sin | 0 | 1/2 | 1/√2 | √3/2 | 0 |
cos | 1 | √3/2 | 1/√2 | 1/2 | 0 |
tan | 0 | 1/√3 | 1 | √3 | Undefined |
cot | Undefined | √3 | 1 | 1/√3 | 0 |
sec | 1 | 2/√3 | √2 | 2 | Undefined |
cosec | Undefined | 2 | √2 | 2/√3 | 1 |
Trigonometry Table For 180°, 270° And 360°
Let us also look at the values of these trigonometric ratios for 180°, 270°, and 360°.
Angles in Degrees | 180° | 270° | 360° |
Angles in Radians | π | 3π/2 | 2π |
sin | 0 | -1 | 0 |
cos | -1 | 0 | 1 |
tan | 0 | Undefined | 1 |
cot | Undefined | 0 | Undefined |
sec | -1 | Undefined | 1 |
cosec | Undefined | -1 | Undefined |
How To Learn Trigonometry Table: Trick To Learn Trigonometric Ratios Table | Trigonometry Table Trick
Memorizing the trigonometry ratio table can help you solve various problems easily. So, if you are looking for trigonometry table tricks, you have come to the right place. Here we will tell you the easy way to learn trigonometry formulas for tables.
If you already know the trigonometry formulas, remembering the trigonometry ratio table will be extremely easy for you. Also, with the formulas at your fingertips, you can calculate the values yourself at any point even if you forget.
Let us first recall and remember trigonometry formulas listed below:
- sin x = cos (90°-x)
- cos x = sin (90°-x)
- tan x = cot (90°-x)
- cot x = tan (90°-x)
- sec x = cosec (90°-x)
- cosec x = sec (90°-x)
- 1/sin x = cosec x
- 1/cos x = sec x
- 1/tan x = cot x
Trigonometry Ratio Table: Determining Values Of Sine Of Standard Angles
Let us assign numbers starting from 0 to each of the standard angles from 0° to 90°:
0° → 0 30° → 1 45° → 2 60° → 3 90° → 4 |
To find the values of the sine of the angles, divide the number corresponding to the angle by 4 and then take the square.
sin0° | \(\sqrt{\frac{0}{4}}=0\) |
sin30° | \(\sqrt{\frac{1}{4}}=1/2\) |
sin45° | \(\sqrt{\frac{2}{4}}=1/√2\) |
sin60° | \(\sqrt{\frac{3}{4}}=√3/2\) |
sin90° | \(\sqrt{\frac{4}{4}}=1\) |
Now, we know the following trigonometry formulas:
sin(π−\(\theta\)) = \(\sin \theta\) ↠ Formula 1 sin(π+\(\theta\)) = -\(\sin \theta\) ↠ Formula 2 sin(2π−\(\theta\)) = -\(\sin \theta\) ↠ Formula 3 |
Using these formulas, let us now find the values of the sine of the angles 180° (π), 270° (3π/2) and 360° (2π) which are in 2nd, third and 4th quadrant respectively:
sin180° = sinπ = sin (π – 0°) = sin0° = 0 (using Formula 1) sin270° = sin(3π/2) = sin (π + 90°) = -sin90° = -1 (using Formula 2) sin360° = sin2π = sin (2π – 0°) = -sin0° = 0 (using Formula 3) |
Trigo Table: Determining Values Of Cosine Of Standard Angles
In order to determine the values of the cosine of standard angles from 0° to 90°, we just assign in the reverse order, i.e.:
0° → 4 30° → 3 45° → 2 60° → 1 90° → 0 |
Now, we divide the number corresponding to the angles by 4 and then take the square.
cos0° | \(\sqrt{\frac{4}{4}}=1\) |
cos30° | \(\sqrt{\frac{3}{4}}=√3/2\) |
cos45° | \(\sqrt{\frac{2}{4}}=1/√2\) |
cos60° | \(\sqrt{\frac{1}{4}}=1/2\) |
cos90° | \(\sqrt{\frac{0}{4}}=0\) |
Now, we know the following trigonometry formulas:
cos(π−\(\theta\)) = -\(\cos \theta\) ↠ Formula 4 cos(π+\(\theta\)) = -\(\cos \theta\) ↠ Formula 5 cos(2π−\(\theta\)) = \(\cos \theta\) ↠ Formula 6 |
Let us now find the values of the cosine of the angles 180° (π), 270° (3π/2) and 360° (2π) using these formulas:
cos180° = cosπ = cos (π – 0°) = -cos0° = -1 (using Formula 4) cos270° = cos(3π/2) = cos (π + 90°) = -cos90° = 0 (using Formula 5) cos360° = cos2π = cos (2π – 0°) = cos0° = 1 (using Formula 6) |
Determining Values Of Tangent Of Standard Angles
We know that:
\(\tan \theta\) = \(\frac{1}{\cot \theta}\) = \(\frac{\sin \theta}{\cos \theta}\) ↠ Formula 7 |
We already know the values of the sine and cosine of the standard angles. Substituting these values in the above formula (Formula 7), we can now easily calculate the values of the tangent of these angles.
tan0° | 0 |
tan30° | 1/√3 |
tan45° | 1 |
tan60° | √3 |
tan90° | Undefined |
tan180° | 0 |
tan270° | Undefined |
tan360° | 1 |
Determining Values Of Cotangent Of Standard Angles
We know that:
\(\cot \theta\) = \(\frac{1}{\tan \theta}\) = \(\frac{\cos \theta}{\sin \theta}\) ↠ Formula 8 |
We know the values of the sine and cosine of the standard angles. Substituting these values in the above formula (Formula 8), we can now easily calculate the values of the cotangent of these angles.
cot0° | Undefined |
cot30° | √3 |
cot45° | 1 |
cot60° | 1/√3 |
cot90° | 0 |
cot180° | Undefined |
cot270° | 0 |
cot360° | Undefined |
Determining Values Of Secant Of Standard Angles
We know:
\(\sec \theta\) = \(\frac{1}{\cos \theta}\) ↠ Formula 9 |
Using the values of the cosine of the standard angles determined above and substituting these values in the above formula (Formula 9), we can now easily calculate the values of the secant of these angles.
sec0° | 1 |
sec30° | 2/√3 |
sec45° | √2 |
sec60° | 2 |
sec90° | Undefined |
sec180° | -1 |
sec270° | Undefined |
sec360° | 1 |
Determining Values Of Cosecant Of Standard Angles
We know that:
\(cosec \theta\) = \(\frac{1}{\sin \theta}\) ↠ Formula 10 |
Using the values of the sine of the standard angles determined above and substituting these values in the above formula (Formula 9), we can now easily calculate the values of the cosecant of these angles.
cosec0° | Undefined |
cosec30° | 2 |
cosec45° | √2 |
cosec60° | 2/√3 |
cosec90° | 1 |
cosec180° | Undefined |
cosec270° | -1 |
cosec360° | Undefined |
Some Important Questions On Trigonometry
Some of the important questions on trigonometry are provided in the table below:
1. Find the value of tan30°/cot60°. |
2. A scalene triangle ABC is given with side AB measuring 10 cm and side BC measuring 5 cm. If, angle C is 59°, find the length of side AC. |
3. A triangle ABC is given. Find the value of a + c√2 if ∠A = 45°, ∠B = 75°. |
4. When the angle of elevation of the sun rays decreases from 60° to 50°, the shadow of a building increases by 10 meters. Calculate the height of the building. |
5. There are two parts of a vertical pole. The lower part is 1/3rd of the whole length. At a point in the horizontal plane through the base of the pole and 20 meters away, the upper part of the pole subtends an angle whose tangent is 1/2. Calculate the possible heights of the pole. |
6. Solve the equation: tan^{-1} 3x + tan^{-1} 2x = π/4 |
7. Calculate the value: tan^{-1} √6 – sec^{-1}(–3) |
8. Calculate the radian value corresponding to 320°. |
9. Calculate the values of trigonometric function cos 457° |
10. Prove the equation: (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0 |
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Trigonometric Table: FAQs On Trigonometry Table
Here we have provided some questions that students search while looking for trigonometric tables:
Ques: What is Trigonometry?
A: The branch of Maths that deals with triangles, its sides, and the different relations between them is referred to as Trigonometry.
Ques: What are the trigonometric functions and their types?
A: The trigonometric functions, also known as circular functions, are the functions of a triangle having one of its angles as 90 degrees. The 6 basic trigonometric functions are:
1) Sine
2) Cos
3) Tan
4) Cot
5) Cosec
6) Sec
Ques: How to find the value of trigonometric functions?
A: To find the vales of different trigonometric functions you can use the below formulas:
i) Sine = Perpendicular/Hypotenuse
ii) Cos = Base/Hypotenuse
iii) Tan = Perpendicular/Base
iv) Cosec = 1/Sin
v) Sec = 1/Cos
vi) Cot = 1/Tan
Ques: What is the value of sin 30 in trigonometry?
A: The value of Sin 30 is 1/2.
So, now you know the values of the trigonometric functions of standard angles from 0° to 360°. You also know how to create and memorize the trigonometry table.
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Go through this article and memorize the necessary trigonometry formulas. Then create the trigonometry table on your own.
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