**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. It has a vast 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.

Trigonometric 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 trigonometric ratios of standard angles are essential to solve the trigonometry problems. Therefore, it is necessary to remember the values of the trigonometric ratios of these standard angles.

The trigonometric table is useful in the number of areas. It 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. Another important application of trigonometric tables is the Fast Fourier Transform (FFT) algorithms.

Trigonometry Ratios 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 |

cosec | 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 ratios table is dependent upon the trigonometry formulas.

Below are the few steps to memorize the trigonometry table.

Before beginning, try to 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 = cosec x
- 1/cos x = sec x
- 1/tan x = cot x

**Steps to Create a 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 the 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 the sin angle. To determine the value of cos divide by 4 in the 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 at 0Â°Â divide the value of sin at 0Â°Â by the value of cos at 0Â°Â See example below.

tan 0Â°= 0/1 = 0

Similarly, 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 is equal to the reciprocal of tan. The value of cot at 0Â° will obtain by dividing 1 by the value of tan at 0Â°. So the value will be:

cot 0Â° = 1/0 = Infinite or Not Defined

Same way, the table for a cot is given 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 at 0Â°Â is the reciprocal of sin at 0Â°.

cosec 0Â°= 1/0 = Infinite or Not Defined

Same way, the table for cosec is given below.

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

cosec | 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 values of cos. The value of sec on \(0^{\circ }\) is the opposite of cos on \(0^{\circ }\). So the value will be:

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

In the same way, the table for sec is given 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:

- Sin 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 values can be easily found by using the following relations:

- Sin =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

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