# Value of Cos 120

When we study the relationship between angles and sides of a triangle, it is called Trigonometry. Trigonometry is used in almost all fields. These applications include engineering, phonetics or game development, and so on. In all these areas, we use trigonometry functions for various purposes. The values of these functions like the value of Cos 120 or Cos 0 is important in these fields.

Value of Cos 120 is -½. |

It has many other applications too. In some cases, it is used indirectly. For example, in creating computer music as sound travels in the form of waves. These waves follow a pattern of sine or cosine functions to develop computer music.

## How to find the value of Cos 120^{0}

As mentioned in the solution given below, 120° can be represented in terms of two angles i.e. either 90° or 180°.

We can show that 120 degrees can be represented in two angles, whose value can be taken from trigonometry table.

90 degree and 180 degree

180° – 60° = 120° ———– (1)

90° + 30° = 120° ———— (2)

Let’s use these now.

Cos 120° = cos(180° – 60°) = – cos 60° = -½ (since cos(180° – x) = – cos x)

Cos 120° = cos(90° + 30°) = – sin 30° = -½ (we know that cos (90° + x) = -sin x)

## Cos 120

Other trigonometric ratios for different angles are:

Trigonometry Ratio Table |
||||||||

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 | Not Defined | 0 | Not Defined | 0 |

cot | Not Defined | √3 | 1 | 1/√3 | 0 | Not Defined | 0 | Not Defined |

cosec | Not Defined | 2 | √2 | 2/√3 | 1 | Not Defined | −1 | Not Defined |

sec | 1 | 2/√3 | √2 | 2 | Not Defined | −1 | Not Defined | 1 |

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