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°
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.
|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|
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.