Cosec 360 Degrees

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

• Cosec 360°: undefined(∞)
• Cosec (-360 degrees): undefined
• Cosec 360° in radians: cosec (2π) or cosec (6.2831853 . . .)

What is the Value of Cosec 360 Degrees?

The value of cosec 360 degrees is undefined(∞). Cosec 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 . . .
∴ cosec 360° = cosec(6.2831) = undefined(∞)

Explanation:

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

Methods to Find Value of Cosec 360 Degrees

The value of cosec 360° is given as undefined(∞). We can find the value of cosec 360 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cosec 360 Degrees Using Unit Circle

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

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

Hence the value of cosec 360° = 1/y = undefined

Cosec 360° in Terms of Trigonometric Functions

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

• ± 1/√(1-cos²(360°))
• ± √(1 + tan²(360°))/tan 360°
• ± √(1 + cot²(360°))
• ± sec 360°/√(sec²(360°) - 1)
• 1/sin 360°

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

• cosec(180° - 360°) = cosec(-180°)
• -cosec(180° + 360°) = -cosec 540°
• sec(90° - 360°) = sec(-270°)
• -sec(90° + 360°) = -sec 450°

Note: Since 360° lies on the positive x-axis, the final value of cosec 360° is undefined.

☛ Also Check:

• cosec 20 degrees
• cosec 2 degrees
• cosec 360 degrees
• cosec 0 degrees
• cosec 150 degrees
• cosec 45 degrees

FAQs on Cosec 360 Degrees

What is Cosec 360 Degrees?

Cosec 360 degrees is the value of cosecant trigonometric function for an angle equal to 360 degrees. The value of cosec 360° is undefined(∞).

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

We can represent the cosec function in terms of the cotangent function using trig identities, cosec 360° can be written as √(1 + cot²(360°)). Here, the value of cot 360° is equal to undefined(∞).

What is the Value of Cosec 360° in Terms of Sec 360°?

Since the cosec function can be represented using the secant function, we can write cosec 360° as sec 360°/√(sec²(360°) - 1). The value of sec 360° is equal to 1.

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

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

• ± 1/√(1-cos²(360°))
• ± √(1 + tan²(360°))/tan 360°
• ± √(1 + cot²(360°))
• ± sec 360°/√(sec²(360°) - 1)
• 1/sin 360°

☛ Also check: trigonometric table

How to Find the Value of Cosec 360 Degrees?

The value of cosec 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 cosec 360° is equal to the reciprocal of the y-coordinate (0). ∴ cosec 360° = undefined(∞).