**Cos 120 **has -1/2 or -0.5 values as it lies in the 2nd quadrant where cos is negative. Cos is one of the 6 trigonometric functions and is widely used in mathematics and physics.

In this article, we will provide you with all the details on the values of cos 120 and other cos values at different angles. We will also provide you with an explanation as to how the value is calculated.

## Cos 120 Value

To find the value of cos 120 we will require a right-angled triangle (refer to the image below) and either of the two formulas i.e. cos (180° – θ) = – cosθ or cos (90° + θ) = – sinθ.

You must already know that cosθ = \(\frac{base}{hypotenuse}\) = \(\frac{b}{h}\)

In your exams the values of a, b, h will be mentioned, and based on these you can calculate cosθ.

Since we are already aware of the trigonometric angle values for sin, cos and tan from 0 to 90. We will use the formula to find the value of cos 120.

Degrees | 0° | 30° | 45° | 60° | 90° |

Sin | 0 | 1/2 | 1/√2 | √3/2 | 1 |

Cos | 1 | √3/2 | 1/√2 | 1/2 | 0 |

Tan | 0 | 1/√3 | 1 | √3 | ∞ |

Using cos (180° – θ) = – cosθ

- Cos 120° = cos (180° – 60°) = -cos 60 = -1/2.

Using cos (90° + θ) = – sinθ

- Cos (90° + 30°) = – sin30° = -1/2.

### Trigonometry Table: Cos 120

Now that you know the value of cosine 120°, let us provide you with the complete trigonometric table:

Angles | 0° | 30° or π/6 | 45° or π/4 | 60° or π/3 | 90° or π/2 | 120° or 2π/3 | 180° or π | 270° or 3π/2 | 360° or 2π |

Sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | √3/2 | 0 | −1 | 0 |

Cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | -1/2 | −1 | 0 | 1 |

Tan | 0 | 1/√3 | 1 | √3 | Not Defined | -√3 | 0 | Not Defined | 0 |

Cot | Not Defined | √3 | 1 | 1/√3 | 0 | -1/√3 | Not Defined | 0 | Not Defined |

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

Sec | 1 | 2/√3 | √2 | 2 | Not Defined | -2 | −1 | Not Defined | 1 |

### Learn On Embibe

Students can access the following free study materials on Embibe for their exam preparation:

NCERT Solutions | NCERT Books |

Class 8 Mock Test Series | Class 8 Practice Questions |

Class 9 Mock Test Series | Class 9 Practice Questions |

Class 10 Mock Test Series | Class 10 Practice Questions |

JEE Main Mock Tests (Class 11-12 PCM) | JEE Main Practice Questions (Class 11-12 PCM) |

NEET Mock Tests (Class 11-12 PCB) | NEET Practice Questions (Class 11-12 PCB) |

### Trigonometric Identities

Here are some identities based on which questions are asked:

**a)**sin (90° – A) = cos A**b)**cos (90° – A) = sin A,**c)**tan (90° – A) = cot A,**d)**cot (90° – A) = tan A,**e)**sec (90° – A) = cosec A,**f)**cosec (90° – A) = sec A,

### Sample Questions

**i)**Evaluate cos 48° – sin 42°.**ii)**Find cosec 31° – sec 59°.**iii)**Solve cos 38° cos 52° – sin 38° sin 52° = 0.**iv)**Evaluate sin 60° cos 30° + sin 30° cos 60°.**v)**2 tan^{2}45° + cos^{2}30° – sin^{2}60°.**vi)**Express the ratios cos A, tan A and sec A in terms of sin A.

### FAQs On Value Of Cos 120 Degree

Here are some questions that are generally searched on the topic.

Q. How do you find cos 120 without a calculator? You can use the formulas Ans. i) cos (180° – θ) = – cosθ or ii) cos (90° + θ) = – sinθ. To find the cos 120. |

Q. What is cos 120 in radians? In radian, the value of cos 120 is 2π/3 i.e equal to -1/2. Ans. |

Q. How do you evaluate cos 120? The method to evaluate cosine 120 has been provided on this page.Ans. |

Q. What is the value of cos 150 degrees? Cos 15 equals -√3/2. Ans. |

*After providing you with all the information on cos 120 we have reached the end of our article and we hope the information was helpful. However, if you have further questions feel free to use the comments section.*

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