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Cosec 0 Degrees
The value of cosec 0 degrees is undefined(∞). Cosec 0 degrees in radians is written as cosec (0° × π/180°), i.e., cosec (0π) or cosec (0). In this article, we will discuss the methods to find the value of cosec 0 degrees with examples.
 Cosec 0°: undefined(∞)
 Cosec (0 degrees): undefined
 Cosec 0° in radians: cosec (0π) or cosec (0 . . .)
What is the Value of Cosec 0 Degrees?
The value of cosec 0 degrees is undefined(∞). Cosec 0 degrees can also be expressed using the equivalent of the given angle (0 degrees) in radians (0 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 0 degrees = 0° × (π/180°) rad = 0π or 0 . . .
∴ cosec 0° = cosec(0) = undefined(∞)
Explanation:
For cosec 0 degrees, the angle 0° lies on the positive xaxis. Thus, cosec 0° value = undefined(∞)
Since the cosecant function is a periodic function, we can represent cosec 0° as, cosec 0 degrees = cosec(0° + n × 360°), n ∈ Z.
⇒ cosec 0° = cosec 360° = cosec 720°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(0°) = cosec(0°) = undefined.
Methods to Find Value of Cosec 0 Degrees
The value of cosec 0° is given as undefined(∞). We can find the value of cosec 0 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cosec 0 Degrees Using Unit Circle
To find the value of cosec 0 degrees using the unit circle:
 Draw the radius of the unit circle, ‘r’ to form 0° angle with the positive xaxis.
 The cosec of 0 degrees equals the reciprocal of the ycoordinate(0) of the point of intersection (1, 0) of unit circle and r.
Hence the value of cosec 0° = 1/y = undefined(∞)
Cosec 0° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cosec 0 degrees as:
 ± 1/√(1cos²(0°))
 ± √(1 + tan²(0°))/tan 0°
 ± √(1 + cot²(0°))
 ± sec 0°/√(sec²(0°)  1)
 1/sin 0°
We can use trigonometric identities to represent cosec 0° as,
 cosec(180°  0°) = cosec 180°
 cosec(180° + 0°) = cosec 180°
 sec(90°  0°) = sec 90°
 sec(90° + 0°) = sec 90°
Note: Since 0° lies on the positive xaxis, the final value of cosec 0° is undefined.
☛ Also Check:
Examples Using Cosec 0 Degrees

Example 1: Find the value of (sec 0° cosec 0°)/2. [Hint: Use cosec 0° = undefined(∞)]
Solution:
(sec 0° cosec 0°)/2 = undefined 
Example 2: Find the value of csc 0° if sin 0° is 0.
Solution:
Since, csc 0° = 1/sin 0°
⇒ csc 0° = 1/0 = undefined 
Example 3: Simplify: 5 (cosec 0°/cosec 90°)
Solution:
We know cosec 0° = undefined and cosec 90° = 1
⇒ 5 cosec 0°/cosec 90° = undefined
FAQs on Cosec 0 Degrees
What is Cosec 0 Degrees?
Cosec 0 degrees is the value of cosecant trigonometric function for an angle equal to 0 degrees. The value of cosec 0° is undefined.
How to Find Cosec 0° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cosec 0° can be given in terms of other trigonometric functions as:
 ± 1/√(1cos²(0°))
 ± √(1 + tan²(0°))/tan 0°
 ± √(1 + cot²(0°))
 ± sec 0°/√(sec²(0°)  1)
 1/sin 0°
☛ Also check: trigonometry table
What is the Exact Value of Cosec 0 Degrees?
The exact value of cosec 0 degrees is undefined(∞).
What is the Value of Csc 0 Degrees in Terms of Cos 0°?
Using trigonometric identities, we can write csc 0° in terms of cos 0° as, csc(0°) = 1/√(1  cos²(0°)). Here, the value of cos 0° is equal to 1.
How to Find the Value of Cosec 0 Degrees?
The value of cosec 0 degrees can be calculated by constructing an angle of 0° with the xaxis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of cosec 0° is equal to the reciprocal of the ycoordinate (0). ∴ cosec 0° = undefined(∞).
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