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The value of cos 120 degrees is -0.5. In trigonometry, cosine (cos) is a trigonometric function that relates the length of the adjacent side of a right-angled triangle to the hypotenuse. When we calculate the cosine of 120 degrees, we find that it equals -0.5. This value signifies that the x-coordinate of a point on the unit circle corresponding to an angle of 120 degrees is -0.5. Cos 120 degrees is commonly used in mathematics, physics, and engineering to solve problems involving obtuse angles, vector calculations, and geometric configurations. Understanding the value of cos 120 degrees is essential in various real-life applications, such as analyzing forces in physics or determining angles in engineering designs.

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

Cos 120 Value can be found out as follows :

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 trigonometric 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)

Some fun facts about cos 120 degrees include that its value is approximately 0.5, it is equal to the sine of 60 degrees, and its value can be calculated using the Pythagorean theorem. Additionally, cosine 120 degrees is often used in trigonometric identities and equations, and is a key component in the calculation of angles in triangles.

### 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 |

- Cosine is an important trigonometric function with many applications in mathematics and physics. Here are some fun facts about cosine:
- Cosine is one of the basic trigonometric functions, along with sine and tangent.
- The cosine of an angle is equal to the sine of the complementary angle.
- cosine function can be used to calculate the length of a side of a right triangle.
- The cosine function is periodic, with a period of 2pi.
- cosine function is even, meaning that cos(-x) = cos(x).
- The graph of the cosine function is a symmetrical curve.
- cosine function is used in many branches of mathematics and physics, including geometry, calculus, and wave theory.

**Related Links**

Cos 30 Degree |
Value of Sin 180 |

Sin 60 Degree |
Sin 120 |

Sin Cos Tan Values |
Cos 90 Value |

**Frequently Asked Questions (FAQs) on Value of Cos 120**

### What is the value of cos 120 degrees?

The value of cos 120 degrees is -0.5.

### How is the value of cos 120 degrees calculated?

Cos 120 degrees is calculated using trigonometric principles, particularly the unit circle. It is the cosine of the angle formed by rotating 120 degrees counterclockwise from the positive x-axis.

### What is the significance of cos 120 degrees?

Cos 120 degrees is a key trigonometric value, widely used in mathematics, physics, and engineering to solve problems involving angles and distances.

### In which geometric configurations is cos 120 degrees commonly used?

Cos 120 degrees frequently appears in problems involving obtuse angles, triangles, and vector calculations.

### What is the complementary angle of cos 120 degrees?

The complementary angle of cos 120 degrees is cos 60 degrees, which also has a value of 0.5.

### How does cos 120 degrees relate to other trigonometric functions?

Cos 120 degrees is related to sin 120 degrees through the Pythagorean trigonometric identity: sin²θ + cos²θ = 1.

### Is cos 120 degrees commonly used in real-life applications?

Yes, cos 120 degrees is used in various real-life applications, including calculating forces in physics, angles in engineering, and angles of rotation in computer graphics.