Trigonometry Table: Trigonometry Table comprises the values of various trigonometric ratios for standard angles – 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 table so that you can directly use them to solve problems.
Trigonometry Table
As mentioned above, the trigonometry table contains the values of trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) of standard angles. Let us first have a look at the 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 Memorize Trigonometry Table?
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.
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.
We will explain all these in the next sections.
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 root.
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) |
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 root.
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 |
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.
Go through this article and memorize the necessary trigonometry formulas. Then create the trigonometry table on your own.
We hope this detailed article on trigonometry table helps you. If you have any query, feel free to ask in the comment section below. We will get back to you at the earliest.
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