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 x-y 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.
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.
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 this 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, we conclude that,
Cos 360° = cos 2π = 1
Cos 360 Degrees Identities
- cos360° = sin (90°+360°) = sin 450°
- cos360° = sin (90°-360°) = sin -270°
- -cos360° = cos (180°+360°) = cos 540°
- -cos360° = cos (180°-360°) = cos -180°
Find the below table to know the values of all the trigonometry ratios.
Trigonometry Table |
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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 |
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