The cosine of 360 degrees or cos 360° represents the angle in the fourth quadrant, angle 360° is greater than 270° and less than or equal to 360°. Also, 360° denotes full rotation in a xy-plane. The value of cos in the fourth quadrant, i.e. 270° to 360°, is always positive. Hence, cos 360° 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 a 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 fourth quadrant, where cos is always positive.
So, cos(360° – θ) = cos θ
Cos 360 + Theta
The value of cos 360 + theta can be calculated 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 cos is also positive.
So, cos(360° + θ) = cos θ
Therefore, the value of cos 360 + theta is equal to cos theta.
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