Trigonometry Table in Maths: Trigonometric Ratios & Functions Table

Trigonometry is an important branch of mathematics dealing with the study of the relationship between length and angles. Usually, trigonometry is associated with right-angled triangles. A right angle is obtained when one of the angles is 90°. Trigonometry plays a vital role in many domains of mathematics. With the help of a trigonometric table, various geometric calculations can be easily worked out. This table consists of trigonometric functions and formulae based on specific angles.

The trigonometric ratios table provides great help to find the values of standard angles, namely 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360°. This table is made up of trigonometric ratios such as sine, cosine, tangent, cosecant, secant and cotangent. The short forms of these ratios are sin, cos, tan, cosec, sec, and cot. The values contained in all these standard angles are necessary to solve the trigonometry problems. The values can easily be remembered with the help of some simple tricks.

What to know more about Trigonometric Identities? Visit our Maths important concept page.

This table is very helpful in different fields. It is mainly essential in navigation, oceanography, astronomy, science, and engineering. Interestingly, this method has been very effectively used in the pre-digital era, where there were no pocket calculators. Moreover, this table has also led to the development of the first mechanical computing devices. It also plays a key role in the foundation of the Fast Fourier Transform (FFT) algorithms.

Trigonometry Ratios Table

Remembering the ratio table can be very useful. It will be much easier to remember the table if one understands the trigonometric formulae, which are also known as trigonometric equations.

Following are the formulae -

• sin x = cos (90° - x)
• cos x = sin (90° - x)
• tan x = cot (90° - x)
• cosec x = sec (90° - x)
• sec x = cosec (90° - x)
• cot x = tan (90° - x)
• 1/sin x = cosec x
• 1/cos x = sec x
• 1/tan x = cot x

Given below are the formulae for 6 important trigonometric functions:

Trigonometric ratios are easily calculated with the help of these 6 formulae describing important trigonometric functions.

Trigonometry is a fundamental branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right-angled triangles. It has broad applications in various fields such as physics, engineering, architecture, and computer science. At the heart of trigonometry lies the trigonometric functions, which are critical for understanding the properties of angles and their corresponding sides. The trigonometry table is an essential tool that provides the values of these trigonometric functions for specific angles. This guide delves into the significance of the trigonometry table, its construction, and its applications.

FAQs: Trigonometry Table in Maths

1. What is a Trigonometry Table?

A trigonometry table is a chart that lists the values of trigonometric functions (sine, cosine, tangent, etc.) for standard angles like 0°, 30°, 45°, 60°, and 90°. It helps in solving trigonometric problems by providing quick reference to these values.

2. What are the key trigonometric functions included in the table?

The key trigonometric functions included in a trigonometry table are:

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

3. Why is the Trigonometry Table important in mathematics?

The trigonometry table is crucial because it allows students and professionals to quickly find the values of trigonometric functions for specific angles. This is essential in solving problems in geometry, physics, engineering, and other mathematical applications.

4. How is the Trigonometry Table used in solving problems?

The trigonometry table is used to find the values of trigonometric functions without the need for a calculator. By referencing the table, one can quickly substitute the values into equations to solve for unknowns in trigonometric problems.

5. What are the standard angles used in a Trigonometry Table?

The standard angles commonly used in a trigonometry table are:

• 0°
• 30°
• 45°
• 60°
• 90°

6. How do you memorize the Trigonometry Table?

Memorizing the trigonometry table can be achieved through practice and mnemonic devices. For example, the sine and cosine values of common angles can be remembered using the square root method or specific patterns.

7. Can the Trigonometry Table be used for angles other than the standard ones?

For non-standard angles, the trigonometric values are often calculated using a calculator or trigonometric identities. However, for standard angles, the table provides exact values that are widely used in various applications.

8. What is the relationship between sine and cosine in the Trigonometry Table?

In the trigonometry table, the sine and cosine values of complementary angles (e.g., 30° and 60°) are equal. For example, sin(30°) = cos(60°) and vice versa. This relationship is based on the co-function identity in trigonometry.

9. How does the Trigonometry Table relate to the unit circle?

The trigonometry table is closely related to the unit circle, where the values of sine, cosine, and tangent for different angles correspond to the coordinates and slopes of points on the unit circle.

10. Are there any tools or apps available for referencing the Trigonometry Table?

Yes, there are many online tools, apps, and calculators that provide quick access to trigonometric tables and functions. These tools are helpful for students and professionals who need to reference trigonometric values frequently.