Trigonometry table is a fundamental tool in mathematics that provides the standard values of trigonometric ratios sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot) at specific angles such as 0°, 30°, 45°, 60°, and 90°.
This maths trigonometry table is especially useful for solving problems in geometry, physics, and engineering. It helps students memorize and quickly reference values, making calculations more efficient.
Sin Cos Tan Formula
The trigonometry table formula follows patterns based on square roots and simple fractions, allowing for easy derivation and understanding of the values. Mastery of this table is essential for anyone studying trigonometry.
What is a Trigonometry Table?
A trigonometry table is a tabular representation of the values of the six trigonometric functions:
-
Sine (sin)
-
Cosine (cos)
-
Tangent (tan)
-
Cosecant (cosec)
-
Secant (sec)
-
Cotangent (cot)
|
Trigonometry Table
|
|
θ (Angle)
|
0° (0)
|
30° (π/6)
|
45° (π/4)
|
60° (π/3)
|
90° (π/2)
|
180° (π)
|
270° (3π/2)
|
360° (2π)
|
|
sin θ
|
0
|
1/2
|
1/√2
|
√3/2
|
1
|
0
|
-1
|
0
|
|
cos θ
|
1
|
√3/2
|
1/√2
|
1/2
|
0
|
-1
|
0
|
1
|
|
tan θ
|
0
|
1/√3
|
1
|
√3
|
∞
|
0
|
∞
|
0
|
|
csc θ (cosec)
|
∞
|
2
|
√2
|
2/√3
|
1
|
∞
|
-1
|
∞
|
|
sec θ
|
1
|
2/√3
|
√2
|
2
|
∞
|
-1
|
∞
|
1
|
|
cot θ
|
∞
|
√3
|
1
|
1/√3
|
0
|
∞
|
0
|
|
Trigonometry Table 0 to 90 Degrees
Here are the standard trigonometric ratios for angles from 0° to 90° that help in solving various mathematical and real-world problems
|
Trigonometry Table 0 to 90 Degrees
|
|
Angle (θ)
|
sin θ
|
cos θ
|
tan θ
|
cosec θ
|
sec θ
|
cot θ
|
|
0°
|
0
|
1
|
0
|
∞
|
1
|
∞
|
|
30°
|
1/2
|
√3/2
|
1/√3
|
2
|
2/√3
|
√3
|
|
45°
|
1/√2
|
1/√2
|
1
|
√2
|
√2
|
1
|
|
60°
|
√3/2
|
1/2
|
√3
|
2/√3
|
2
|
1/√3
|
|
90°
|
1
|
0
|
∞
|
1
|
∞
|
0
|
Trigonometry Table 0° to 360°
Trigonometric ratios of standard angles are essential for solving various problems in mathematics and physics.
Below is the complete trigonometry table for angles from 0° to 360°, showing the values of sin, cos, tan, cot, sec, and cosec.
|
Trigonometry Table 0° to 360°
|
|
Angle (°)
|
sin θ
|
cos θ
|
tan θ
|
cot θ
|
sec θ
|
cosec θ
|
|
0°
|
0
|
1
|
0
|
∞
|
1
|
∞
|
|
30°
|
1/2
|
√3/2
|
1/√3
|
√3
|
2/√3
|
2
|
|
45°
|
1/√2
|
1/√2
|
1
|
1
|
√2
|
√2
|
|
60°
|
√3/2
|
1/2
|
√3
|
1/√3
|
2
|
2/√3
|
|
90°
|
1
|
0
|
∞
|
0
|
∞
|
1
|
|
120°
|
√3/2
|
-1/2
|
-√3
|
-1/√3
|
-2
|
2/√3
|
|
135°
|
1/√2
|
-1/√2
|
-1
|
-1
|
-√2
|
√2
|
|
150°
|
1/2
|
-√3/2
|
-1/√3
|
-√3
|
-2/√3
|
2
|
|
180°
|
0
|
-1
|
0
|
∞
|
-1
|
∞
|
|
210°
|
-1/2
|
-√3/2
|
1/√3
|
√3
|
-2/√3
|
-2
|
|
225°
|
-1/√2
|
-1/√2
|
1
|
1
|
-√2
|
-√2
|
|
240°
|
-√3/2
|
-1/2
|
√3
|
1/√3
|
-2
|
-2/√3
|
|
270°
|
-1
|
0
|
∞
|
0
|
∞
|
-1
|
|
300°
|
-√3/2
|
1/2
|
-√3
|
-1/√3
|
2
|
-2/√3
|
|
315°
|
-1/√2
|
1/√2
|
-1
|
-1
|
√2
|
-√2
|
|
330°
|
-1/2
|
√3/2
|
-1/√3
|
-√3
|
2/√3
|
-2
|
|
360°
|
0
|
1
|
0
|
∞
|
1
|
∞
|
Trigonometry Table Formulas
The values in the table can be derived using these trigonometry table formulas:
1. Basic Trigonometric Ratios
-
sin θ = Opposite / Hypotenuse
-
cos θ = Adjacent / Hypotenuse
-
tan θ = Opposite / Adjacent
-
cosec θ = 1 / sin θ
-
sec θ = 1 / cos θ
-
cot θ = 1 / tan θ
2. Pythagorean Identities
-
sin²θ + cos²θ = 1
-
1 + tan²θ = sec²θ
-
1 + cot²θ = cosec²θ
These formulas are used to verify or calculate missing trigonometric values in the maths trigonometry table.
Inverse Trigonometry Table
When you're given the value of a trigonometric function and asked to find the angle, you use the inverse trigonometry table.
Here are a few examples:
|
Inverse Trigonometry Table
|
|
Function Value
|
Angle θ
|
|
sin⁻¹(1/2)
|
30°
|
|
cos⁻¹(1/2)
|
60°
|
|
tan⁻¹(1)
|
45°
|
|
sin⁻¹(1)
|
90°
|
|
cos⁻¹(0)
|
°
|
The inverse trigonometric table is helpful in geometry and coordinate geometry where you're often solving for unknown angles.
Value Table of Trigonometry
Trigonometry is the branch of mathematics that explores the relationship between the angles and sides of a right-angled triangle. The term trigonometric values refers to the values of specific trigonometric ratios, which include:
-
Sine (sin)
-
Cosine (cos)
-
Tangent (tan)
-
Cosecant (csc)
-
Secant (sec)
-
Cotangent (cot)
How to Use the Trigonometry Table?
Using a trigonometry table can help you quickly find the values of sine, cosine, tangent, and other functions for specific angles. Follow these simple steps to use the table effectively:
-
Identify the angle involved in your problem.
-
Refer to the table to find the value of the required function (sin, cos, tan, etc.).
-
Plug in the value into your equation to simplify and solve.
This process helps save time and avoids the need for calculators in many cases.
Importance of Trigonometry Tables in Maths
Trigonometry tables play a vital role in mathematics by making it easier to work with angles and their functions. Here are some key reasons why they are important:
-
Trigonometry tables are reference tools for quick calculation.
-
They help in understanding the patterns and symmetry of trigonometric functions.
-
These tables are the foundation for trigonometric graphs and calculus applications.
-
Widely used in geometry, physics, architecture, and engineering.
Solved Examples of Trigonometry Table
To better understand how to use trigonometry tables, here are some solved examples demonstrating their practical application in different problems:
Example 1:
Find the value of tan 45o + 2 cos 60o – sec 60o.
Solution:
From the trigonometry table, tan 45o = 1, cos 60o = ½ and sec 60o = 2
Therefore, tan 45o + 2 cos 60o – sec 60o = 1 + 2 × ½ – 2 = 1 + 1 – 2 = 0
Example 2:
Find the value of sin 75o.
Solution:
We can write,
sin 75o = sin (45o + 30o) = sin 45o cos 30o + cos 45o sin 30o
{since, sin (A + B) = sin A cos B + cos A sin B}
= 1/√2 × √3/2 + 1/√2 × 1/2 = (√3 + 1)/2√2
∴ sin 75o= (√3 + 1)/2√2
Example 3:
Using the trigonometric table, evaluate sin2 30o + cos230o.
Solution:
By the trigonometric identities, we know that sin2 𝜃 + cos2 𝜃 = 1. But let us prove this using the trigonometric table.
sin2 30o + cos230o = (½)2 + (√3/2)2 = ¼ + ¾ = 4/4 = 1
