# Cos 360

The cosine of 360 degrees or **cos 360** represents the angle in the fourth quadrant, angle 360 is greater than 270 degrees and less than or equal to 360°. Also, 360 degrees denotes full rotation in an xy-plane. The value of cos in the fourth quadrant, i.e. 270° to 360°, is always positive. Hence, cos 360 degrees is also a positive value. The exact value of cos 360 degrees is 1. Also, learn the value of cos 180 here.

## Cos 360 Value

If we have to write cosine 360° value in radians, then we need to multiply 360° by π/180.

Hence, cos 360° = cos (360 * π/180) = cos 2π

So, we can write, cos 2π = 1

Here, π is denoted for 180°, which is half of the rotation of a unit circle. Hence, 2π denotes full rotation. So, for any number of a full rotation, n, the value of cos will remain equal to 1. Thus, cos 2nπ = 1.

Moreover, we know that cos (-(-θ)) = cos(θ), therefore, even if we travel in the opposite direction, the value of cos 2nπ will always be equal.

However, we can identify the value of cos 360° in unit circle as given below:

## How to Find cos 360 degrees?

We know **the value of** **cos 360° is always equal to 1**. Now, let us find out how we can evaluate the cos 360 degrees value.

As we know, cos 0° = 1

Now, once we take a complete rotation in a unit circle, we reach back to the starting point.

After completing one rotation, the value of the angle is 360° or 2π in radians.

Thus, we can say, after reaching the same position,

Cos 0° = cos 360°

Or

Cos 0° = 2π

Therefore, the Cos 360° value = cos 2π = 1

### Cos 360 Degrees Identities

- cos 360° = sin (90°+360°) = sin 450°
- cos 360° = sin (90°-360°) = sin -270°
- -cos 360° = cos (180°+360°) = cos 540°
- -cos 360° = cos (180°-360°) = cos -180°

Find the below table to know the values of all the trigonometry ratios.

Trigonometry Table |
|||||||||||||

Angles (In Degrees) |
0° |
30° |
45° |
60° |
90° |
120° |
150° |
180° |
210° |
270° |
300° |
330° |
360° |

Angles (In Radians) |
0° |
π/6 |
π/4 |
π/3 |
π/2 |
2π/3 |
5π/6 |
π |
7π/6 |
3π/2 |
5π/3 |
11π/6 |
2π |

sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | √3/2 | 1/2 | 0 | -1/2 | -1 | -√3/2 | -1/2 | 0 |

cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | -1/2 | -√3/2 | -1 | -√3/2 | 0 | 1/2 | √3/2 | 1 |

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

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

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

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

**Also, check:**

### Cos 360 – Theta

Let’s see the value of the expression cos 360 – theta, i.e. cos(360° – θ).

cos(360° – θ) = cos(4 × 90° – θ)

Here, 90° is multiplied by 4, i.e. an even number, so cos will not change in the result. Also, 360° – θ comes in the forth quadrant, where cos is always positive.

So, cos(360° – θ) = cos θ

### Cos 360 + Theta

The value of cos 360 + theta can be calculate as given below:

The value of the expression cos 360 + theta, i.e. cos(360° + θ).

cos(360° + θ) = cos(4 × 90° + θ)

Here, 90° is multiplied by 4, i.e. an even number, so cos will not change in the result. Also, 360° + θ comes in the firth quadrant, where all trigonometric ratios are positive and hence cos is also positive.

So, cos(360° + θ) = cos θ

Therefore, the value of cos 360 + theta is equal to cos theta.