**Contents**hide

## Introduction to Trigonometry

Trigonometry is a mathematical discipline that studies the relationships between angles and sides of triangles. The word “trigonometry” comes from the Greek words for triangle (τρίγωνος) and measure (μέτρος). These relationships are represented by a set of six ratios, called the trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. In this article knowledge glow will, show the Trigonometry Table, Trigonometric Functions, Trigonometric Ratios Table and Steps to Create Trigonometric Table.

The trigonometric functions can be used to solve problems in a variety of fields, including astronomy, engineering, and physics. In addition, these functions can be used to calculate properties of figures such as polygons and circles.

## Trigonometric Values

The Trigonometric value is a collective term for the various ratios values, such as sine, cosine, tangent, secant, cotangent and cosecant in a trigonometric table. All trigonometric ratios are related to the sides of a right triangle and their values are found using the following ratios.

The following lists the values of the six trigonometric functions for angles measured in degrees.

- Sinesin(θ) = opposite / hypotenuse
- Cosinecos(θ) = adjacent / hypotenuse
- Tangenttan(θ) = opposite / adjacent
- Cosecantcsc(θ) = hypotenuse / opposite
- Secantsec(θ) = hypotenuse /

## Trigonometry Table Formula

The Trigonometric formulas or Identities are the equations which are true in the case of Right-Angled Triangles. Some of the special trigonometric identities are given below –

### Pythagorean Identities

- sin²θ + cos²θ = 1
- tan
^{2}θ + 1 = sec^{2}θ - cot
^{2}θ + 1 = cosec^{2}θ - sin 2θ = 2 sin θ cos θ
- cos 2θ = cos²θ – sin²θ
- tan 2θ = 2 tan θ / (1 – tan²θ)
- cot 2θ = (cot²θ – 1) / 2 cot θ

### Sum and Difference identities-

For angles u and v, we have the following relationships:

- Sin(u + v) = sin(u)cos(v) + cos(u)sin(v)
- Cos(u + v) = cos(u)cos(v) – sin(u)sin(v)
- Tan(u+v)=tan(u)+tan(v)/1-tan(u) tan (v)
- Sin(u – v) = sin(u)cos(v) – cos(u)sin(v)
- Cos(u – v) = cos(u)cos(v) + sin(u)sin(v)
- Tan(u-v) = tan(u) – tan(v)/1 + tan(u) tan (v)

If A, B and C are angles and a, b and c are the sides of a triangle, then,

### Sine Laws

- a/sinA = b/sinB = c/sinC

### Cosine Laws

- c
^{2 }= a^{2 }+ b^{2 }– 2ab cos C - a
^{2 }= b^{2 }+ c^{2 }– 2bc cos A - b
^{2 }= a^{2 }+ c^{2 }– 2ac cos B

## Trigonometric Functions

The trigonometric functions are some of the most important functions in mathematics. They arise in many different contexts, from geometry to physics. Here, we’ll take a look at what trigonometric functions are and how they can be used.

Trigonometric functions are functions of an angle. The most basic trigonometric function is the sine function, which gives the ratio of the length of the side opposite to an angle in a right-angled triangle to the length of the hypotenuse. The other two basic trigonometric functions are the cosine and tangent functions, which give the ratios of the other two sides of a right-angled triangle to the length of the hypotenuse.

These three functions can be used to solve problems in many different areas of mathematics and physics. For example, they can be used to calculate lengths and angles in triangles, to understand wave motion, and to solve problems involving projectile motion.

There are many other trigonometric functions that can be defined, depending on what you want to do with them. In general, though, all of these functions will be defined in terms of the six trigonometric functions.

### Six Important Trigonometric Functions (Trigonometric Ratios)

These six trigonometric functions (trigonometric ratios) are solved by using the below formulas. It’s very important to get the knowledge about sides of the right triangle because it’s definitely the set of trigonometric functions.

Functions | Abbreviation | Relationship to sides of a right triangle |

Sine Function | sin | Opposite side/ Hypotenuse |

Tangent Function | tan | Opposite side / Adjacent side |

Cosine Function | cos | Adjacent side / Hypotenuse |

Cosecant Function | cosec | Hypotenuse / Opposite side |

Secant Function | sec | Hypotenuse / Adjacent side |

Cotangent Function | cot | Adjacent side / Opposite side |

## Trigonometry Table

If you’re studying trigonometry, then you know that a big part of the subject is memorizing a lot of information. Trigonometry tables can be a big help when it comes to memorization, and in this blog post we’ll give you a trigonometry table to help you out. We’ll also explain some of the steps involved in using a trigonometry table.

First, let’s take a look at the trigonometry table. This table lists the six most common trigonometric functions and their values for various angles.

**Angle (degrees) 0 30 45 60 90**

- sin 0 0.5 0.7 0.8 1
- cos 1 0.8 0.7 0.5 0
- tan 0 0.6 1.0 1.7 –
- sec 1 1.7 1.0 0.6 –
- csc – 1.0 1/6 – –
- cot – 1/6 1.0 – –

## Trigonometry Table 0-360 ( Trigonometric Table)

## How to Use the Trigonometry Table

The trigonometry table is a great tool for quickly finding the values of common trigonometric functions. To use the table, simply find the angle you’re interested in on the left hand side, and then find the function you’re interested in on the top row. The value at the intersection of your angle and function will be the value you’re looking for.

For example, suppose you want to find the value of cos(60). Looking at the table, you can see that cos(60) is equal to 0.5.

You can also use the trigonometry table to quickly find the values of inverse trigonometric functions. For example, suppose you want to find the value of sin^-1(0.5). Looking at the table, you can see that sin^-1(0.5) is equal to 60.

Finally, you can use the trigonometry table to quickly find the values of complex exponential functions. For example, suppose you want to find e^{i*60}. Looking at the table, you can see that e^{i*60} is equal to 0.5+0.86603i.

## Steps for Finding Values in the Trigonometry Table

1. Locate the angle you are working with on the outside of the table.

2. Find the row in the table that corresponds to that angle.

3. Find the column in the table that corresponds to the function you are looking for (sine, cosine, tangent, etc.).

4. The value at the intersection of that row and column is the answer to your problem.

## Tricks To Remember Trigonometry Table

We will provde a one-hand trick for remembering the trigonometric table easily! Choose each finger the standard angles as shown in the figure. For filling the sine values in the trigonometry table, we will include counting of the fingers, while for the cos table we will simply fill the values in reverse order.

Step 1: For sin tablecount the fingers from the left side for the standard angle.

Step 2: Divide the result of above step by 4

Step 3: Take the square root of ratio.

Given below is a list of trigonometric formulas that helps to memorize the trigonometric table, based on the relationship between different types of trigonometric ratios.

- 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
- 1/cot x = 1/sec x

## Trigonometry Ratios Table

The trigonometry ratios table (shown below) is a reference for the trig functions and their corresponding angle measurements. The angle measurements are also known as “trigonometric functions” and you can use them to determine the value of a triangle based on its sides.

Angles (In Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |

Angles (In Radians) | 0° | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |

sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | -1 | 0 |

cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | -1 | 0 | 1 |

tan | 0 | 1/√3 | 1 | √3 | ∞ | 0 | ∞ | 0 |

cot | ∞ | √3 | 1 | 1/√3 | 0 | ∞ | 0 | ∞ |

cosec | ∞ | 2 | √2 | 2/√3 | 1 | ∞ | -1 | ∞ |

sec | 1 | 2/√3 | √2 | 2 | ∞ | -1 | ∞ | 1 |

## Steps to Create a Trigonometry Table

*Trigonometric table covers the value of trigonometric ratios for all basic angles ranging from 0º to 360º.*

**Step 1: ** Create a table with the top row listing the angles.**such as **0°, 30°, 45°, 60°, 90°, and then write all trigonometric functions in the first column such as sin, cos, tan, cosec, sec, cot.

**Step 2: **Determining the value of sin: Write the angles 0°, 30°, 45°, 60°, 90° in ascending order and assign them values 0, 1, 2, 3, 4 according to the order. So, 0° ⟶ 0; 30° ⟶ 1; 45° ⟶ 2; 60° ⟶ 3; 90° ⟶ 4.

Then divide the values by 4 and square root the entire value. 0° ⟶ √0/2; 30° ⟶ 1 /2; 45° ⟶ 1/ √2; 60° ⟶ √3/2; 90° ⟶ √(4/4).

This gives the values of sine for these 5 angles. Now for the remaining three use:

Angles (In Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |

sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | -1 | 0 |

**Step 3:** Determining value of cos: sin (90° – x) = cos x.

Use this formula to compute values for cos x. For example, cos 45° = sin (90° – 45°) = sin 45°. Similarly, cos 30° = sin (90° – 30°) = sin 60°. Using this, you can easily find out the value of cos function as,

Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |

cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | -1 | 0 | 1 |

**Step 4:** Determining the value of tan: (tan x = sin x/cos x). Hence, the value of tan function can be generated as,

Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |

tan | 0 | 1/√3 | 1 | √3 | ∞ | 0 | ∞ | 0 |

**Step 5: **Determining the value of cot: (cot x = 1/tan x). Use the relation to generate the cot function as,

Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |

cot | ∞ | √3 | 1 | 1/√3 | 0 | ∞ | 0 | ∞ |

**Step 6: **Determining the value of cosec: (cosec x = 1/sin x)

Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |

cosec | ∞ | 2 | √2 | 2/√3 | 1 | ∞ | -1 | ∞ |

**Step 7:** Determining the value of sec: (sec x = 1/cos x)

Angles(in Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |

sec | 1 | 2/√3 | √2 | 2 | ∞ | -1 | ∞ | 1 |

## Conclusion

The **trigonometry table** is a very useful tool for solving problems related to trigonometric functions. With the help of this table, you can easily find the values of various trigonometric functions and use them to solve complex problems. This table is an essential part of every mathematics student’s toolkit and it is important to learn how to use it effectively.

## Frequently Asked Questions on Trigonometry

### What Is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of triangles. It includes three basic branches, namely: Trigonometry, Analytic geometry and Calculus.

### What Are the Trigonometric Functions?

The trigonometric functions are used to find out the values of angles in right triangles. They can be applied to all right-angled triangles but they are most useful when applied to acute triangles (90 degrees).

### How to Find the Value of Trigonometric Functions?

To find the value of a trigonometric function, you need to know the angle and any two sides of the triangle. The sine value is found by dividing the opposite side by the hypotenuse; cosine value is found by dividing adjacent side by the hypotenuse, and tangent value is found by dividing opposite side over adjacent side.

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