**Trigonometry Table 0 to 360:** Trigonometry is a branch in Mathematics, which involves the study of the relationship involving the length and angles of a triangle. It is generally associated with a right-angled triangle, where one of the angles is always 90 degrees. The taIt has a wide number of applications in other fields of Mathematics.Â Many geometric calculations can be easily figured out using the table of trigonometric functionsÂ and formulas as well.

The Trigonometrical ratios table helps to find the values of trigonometric standard angles such as 0Â°, 30Â°, 45Â°, 60Â° and 90Â°. It consists of trigonometric ratios – sine, cosine, tangent, cosecant, secant, cotangent. These ratios can be written in short as sin, cos, tan, cosec, sec and cot. The values of trigonometrical ratios of standard angles are very important to solve the trigonometrical problems. Therefore, it is necessary to remember the value of the trigonometrical ratios of these standard angles.

The trigonometric table is useful in the number of areas. ItÂ is essential for navigation, science, and engineering. This table was effectively used in the pre-digital era, even before the existence of pocket calculators. Further, the table led to the development of the first mechanical computing devices.Â Another important application of trigonometric tables is for Fast Fourier Transform (FFT) algorithms.

Trigonometry Ratio Table |
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Angles (In Degrees) |
0Â° | 30Â° | 45Â° | 60Â° | 90Â° | 180Â° | 270Â° | 360Â° |

Angles (In Radians) |
0Â° | Ï€/6 | Ï€/4 | Ï€/3 | Ï€/2 | Ï€ | 3Ï€/2 | 2Ï€ |

sin | 0 | 1/2 | 1/âˆš2 | âˆš3/2 | 1 | 0 | -1 | 0 |

cos | 1 | âˆš3/2 | 1/âˆš2 | 1/2 | 0 | -1 | 0 | 1 |

tan | 0 | 1/âˆš3 | 1 | âˆš3 | âˆž | 0 | âˆž | 0 |

cot | âˆž | âˆš3 | 1 | 1/âˆš3 | 0 | âˆž | 0 | âˆž |

csc | âˆž | 2 | âˆš2 | 2/âˆš3 | 1 | âˆž | -1 | âˆž |

sec | 1 | 2/âˆš3 | âˆš2 | 2 | âˆž | -1 | âˆž | 1 |

**Tricks To Remember Trigonometry Table**

Remembering the trigonometry table will help in many ways, and it is easy to remember the table. If you know the trigonometry formulas then remembering the trigonometry table is very easy. The Trigonometry ratio table is depended upon the trigonometry formulas in a similar way that all the functions of trigonometry are depended on each aspect and interlinked with each other.

Below are the few steps to memorize the trigonometry table.

Before beginning try to remember these values, recall and remember below trigonometry formulas.

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

**Steps to Create Trigonometry Table:**

**Step 1: **

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

**Step 2: Determine the value of sin. **

To determine the values of sin, divide 0, 1, 2, 3, 4 by 4 under the root, respectively. See the example below.

To determine the value of sin 0Â°

\(\sqrt{\frac{0}{4}}=0\)

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

sin | 0 | 1/2 | 1/âˆš2 | âˆš3/2 | 1 | 0 | -1 | 0 |

**Step 3: Determine the value of cos.**

The cos-value is the opposite angle of sin angle. To determine the value of cos divide by 4 in opposite sequence of sin. For example, divide 4 by 4 under the root to get the value of cos 0Â°. See the example below.

To determine the value of cos 0Â°

\(\sqrt{\frac{4}{4}}=1\)

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

cos | 1 | âˆš3/2 | 1/âˆš2 | 1/2 | 0 | -1 | 0 | 1 |

**Step 4: Determine the value of tan.**

The tan is equal to sin divided by cos. tan = sin/cos. To determine the value of tan on 0Â°Â divide the value of sin on 0Â°Â by the value of cos on 0Â°Â See example below.

tan 0Â°= 0/1 = 0

In a similar way, the table would be.

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

tan | 0 | 1/âˆš3 | 1 | âˆš3 | âˆž | 0 | âˆž | 0 |

**Step 5: Determine the value of cot.**

The value of cot can be determined by all opposite value of tan. The value of tan on 0Â° is the opposite of tan on 0Â°. So the value will be:

cot 0Â°=1/0=Infinite or Not Defined

Same way, the table for a cot is below.

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

cot | âˆž | âˆš3 | 1 | 1/âˆš3 | 0 | âˆž | 0 | âˆž |

**Step 6: Determine the value of cosec.**

The value of cosec on 0Â°is the reciprocal of sin on 0Â°.

csc 0Â°= 1/0=Infinite or Not Defined

Same way, the table for cosec is below.

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

csc | âˆž | 2 | âˆš2 | 2/âˆš3 | 1 | âˆž | -1 | âˆž |

**Step 7: Determine the value of sec.**

The value of sec can be determined by all reciprocal value of cos. The value of sec on \(0^{\circ }\) is the opposite of cos on \(0^{\circ }\). So the value will be:

\(\sec 0^{\circ }=\frac{1}{1}=1\)

Same way, the table for sec is below.

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

sec | 1 | 2/âˆš3 | âˆš2 | 2 | âˆž | -1 | âˆž | 1 |

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## Frequently Asked Questions

### What is Trigonometry?

Trigonometry is the branch ofÂ mathematics which deals with the relationship between the sides of a triangle (Right angled triangle) and its angles.

### What are trigonometric functions and its types?

Trigonometric functions or circular functions are defined as the functions of an angle of a right-angled triangle. There are 6 basic types of trigonometric functions which are:

- Sine function
- Cos function
- Tan function
- Cot function
- Cosec function
- Sec function

### How to find the value of trigonometric functions?

All the trigonometric functions are related to the sides of the triangle and their value can be easily found by using the following relations:

- Sine =Â Opposite/Hypotenuse
- Cos =Â Adjacent/Hypotenuse
- Tan =Â Opposite/Adjacent
- Cot = 1/Tan =Â Adjacent/Opposite
- Cosec =Â 1/Sin = Hypotenuse/Opposite
- Sec =Â 1/Cos = Hypotenuse/Adjacent

Very useful .and thank you for much information .