Trigonometric Table

Trigonometry Table 0 to 360: Trigonometry is a part of mathematics that studies the relationship between the angles and sides of a triangle. It is mainly used with a right-angled triangle, where one angle is always 90°. Trigonometry is very useful and is used in many areas of mathematics and real life.

A trigonometry table helps you find the values of trigonometric ratios for common angles like 0°, 30°, 45°, 60°, and 90°. These ratios include:

• Sine (sin)
• Cosine (cos)
• Tangent (tan)
• Cosecant (cosec)
• Secant (sec)
• Cotangent (cot)

These values are important because they make it easier to solve trigonometry problems quickly. That’s why students are often encouraged to learn and remember these standard values.

Trigonometric tables are useful in many fields such as navigation, engineering, and science. Before calculators were invented, people used these tables to do calculations. In fact, these tables also helped in the development of early computers.

Today, trigonometry is still very important and is even used in advanced technologies like signal processing and Fast Fourier Transform (FFT).

What is Trigonometric Table?

The trigonometric table is a simple chart that shows the values of trigonometric ratios for common angles like 0°, 30°, 45°, 60°, and 90°, and sometimes also for angles such as 180°, 270°, and 360°, in a table format. Since these values follow clear patterns, it becomes easier to understand them, remember them, and even predict missing values. This table is very useful as a quick reference when solving math problems involving angles. The main trigonometric functions included in the table are sine, cosine, tangent, cotangent, secant, and cosecant.

Trigonometric Table for Class 10, 11 and 12

Trigonometry Table Formula

The trigonometry table is based on standard formulas used to find values of angles like 0°, 30°, 45°, 60°, and 90°.

Sine (sin θ) Formula Pattern

sin θ = √(n/4)

Where n = 0, 1, 2, 3, 4 for angles: 0°, 30°, 45°, 60°, 90°

Cosine (cos θ) Formula Pattern

cos θ = √((4 − n)/4)

Where n = 0, 1, 2, 3, 4

Tangent (tan θ) Formula

tan θ = sin θ / cos θ

Cosecant (cosec θ) Formula

cosec θ = 1 / sin θ

Secant (sec θ) Formula

sec θ = 1 / cos θ

Cotangent (cot θ) Formula

cot θ = 1 / tan θ

Tricks To Remember Trigonometry Table

Remembering the trigonometry table is very helpful and not as difficult as it may seem. Once you understand the basic trigonometry formulas, learning the table becomes much easier. In fact, the trigonometry table is based on these formulas.

Here are some simple steps that can help you memorize the trigonometry table easily. Before you start, make sure you understand and remember the basic trigonometry formulas.

• 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

Steps to Create a Trigonometry Table

Creating a trigonometry table is easier than memorizing it. Follow these simple steps:

Step 1: Write the Angles

Start by writing the standard angles: 0°, 30°, 45°, 60°, 90°

Step 2: Write Numbers (0 to 4)

Below the angles, write numbers in order: 0, 1, 2, 3, 4

Step 3: Find sin values

Use this formula:

sin θ = √(number ÷ 4)

So:

• sin 0° = √(0/4) = 0
• sin 30° = √(1/4) = 1/2
• sin 45° = √(2/4) = 1/√2
• sin 60° = √(3/4) = √3/2
• sin 90° = √(4/4) = 1

Step 4: Find cos values

For cos, just reverse the sin values:

• cos 0° = 1
• cos 30° = √3/2
• cos 45° = 1/√2
• cos 60° = 1/2
• cos 90° = 0

Step 5: Find tan values

Use the formula:

tan θ = sin θ / cos θ

So:

• tan 0° = 0
• tan 30° = 1/√3
• tan 45° = 1
• tan 60° = √3
• tan 90° = not defined