# Trigonometry Table

**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. Many geometric calculations can be easily figured out using the table of trigonometric functions and formulas as well.

Trigonometric ratios table helps to find the values of trigonometric standard angles such as 0°, 30°, 45°, 60° and 90°. 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) |
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 |

**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 (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:**

**Step 1: **

Create a table with the top row listing the angles such as 0°, 30°, 45°, 60°, 90°, 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 0°

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

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: 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 0°. See the example below.

To determine the value of cos 0°

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

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: Determine the value of tan.**

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

tan 0°= 0/1 = 0

Similarly, the table would be.

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

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

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

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

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

Same way, the table for a cot is given below.

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

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

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

The value of cosec at 0° is the reciprocal of sin at 0°.

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

Same way, the table for cosec is given below.

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

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

**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) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |

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

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## Frequently Asked Questions

### What is Trigonometry?

Trigonometry is the branch of 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 = Opposite/Hypotenuse
- Cos = Adjacent/Hypotenuse
- Tan = Opposite/Adjacent
- Cot = 1/Tan = Adjacent/Opposite
- Cosec = 1/Sin = Hypotenuse/Opposite
- Sec = 1/Cos = Hypotenuse/Adjacent