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Cos 360 Degrees

The value of cos 360 degrees is 1. Cos 360 degrees in radians is written as cos (360° × π/180°), i.e., cos (2π) or cos (6.283185. . .). In this article, we will discuss the methods to find the value of cos 360 degrees with examples.

Cos 360°: 1
Cos (-360 degrees): 1
Cos 360° in radians: cos (2π) or cos (6.2831853 . . .)

What is the Value of Cos 360 Degrees?

The value of cos 360 degrees is 1. Cos 360 degrees can also be expressed using the equivalent of the given angle (360 degrees) in radians (6.28318 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 360 degrees = 360° × (π/180°) rad = 2π or 6.2831 . . .
∴ cos 360° = cos(6.2831) = 1

Explanation:

For cos 360 degrees, the angle 360° lies on the positive x-axis. Thus cos 360° value = 1
Since the cosine function is a periodic function, we can represent cos 360° as, cos 360 degrees = cos(360° + n × 360°), n ∈ Z.
⇒ cos 360° = cos 720° = cos 1080°, and so on.
Note: Since, cosine is an even function, the value of cos(-360°) = cos(360°).

Methods to Find Value of Cos 360 Degrees

The value of cos 360° is given as 1. We can find the value of cos 360 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cos 360° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 360 degrees as:

± √(1-sin²(360°))
± 1/√(1 + tan²(360°))
± cot 360°/√(1 + cot²(360°))
±√(cosec²(360°) - 1)/cosec 360°
1/sec 360°

Note: Since 360° lies on the positive x-axis, the final value of cos 360° will be positive.

We can use trigonometric identities to represent cos 360° as,

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

Cos 360 Degrees Using Unit Circle

To find the value of cos 360 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 0° or 360° angle with the positive x-axis.
The cos of 360 degrees equals the x-coordinate(1) of the point of intersection (1, 0) of unit circle and r.

Hence the value of cos 360° = x = 1

☛ Also Check:

Examples Using Cos 360 Degrees

Example 1: Simplify: 7 (cos 360°/sin 450°)

Solution:

We know cos 360° = sin 450°
⇒ 7 cos 360°/sin 450° = 7 (cos 360°/cos 360°)
= 7(1) = 7
Example 2: Find the value of (cos² 180° - sin² 180°). [Hint: Use cos 360° = 1]

Solution:

Using the cos 2a formula,
(cos² 180° - sin² 180°) = cos(2 × 180°) = cos 360°
∵ cos 360° = 1
⇒ (cos² 180° - sin² 180°) = 1
Example 3: Find the value of 2 cos(360°)/3 sin(-270°).

Solution:

Using trigonometric identities, we know, cos(360°) = sin(90° - 360°) = sin(-270°).
⇒ cos(360°) = sin(-270°)
⇒ Value of 2 cos(360°)/3 sin(-270°) = 2/3

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FAQs on Cos 360 Degrees

What is Cos 360 Degrees?

Cos 360 degrees is the value of cosine trigonometric function for an angle equal to 360 degrees. The value of cos 360° is 1.

What is the Exact Value of cos 360 Degrees?

The exact value of cos 360 degrees is 1.

How to Find Cos 360° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 360° can be given in terms of other trigonometric functions as:

± √(1-sin²(360°))
± 1/√(1 + tan²(360°))
± cot 360°/√(1 + cot²(360°))
± √(cosec²(360°) - 1)/cosec 360°
1/sec 360°

☛ Also check: trigonometric table

What is the Value of Cos 360 Degrees in Terms of Cot 360°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 360° can be written as cot 360°/√(1 + cot²(360°)).

How to Find the Value of Cos 360 Degrees?

The value of cos 360 degrees can be calculated by constructing an angle of 360° with the x-axis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of cos 360° is equal to the x-coordinate (1). ∴ cos 360° = 1.

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