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.