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 x-axis. 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 x-axis.
- The cosec of 0 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 0° = 1/y = undefined(∞)
Cosec 0° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cosec 0 degrees as:
- ± 1/√(1-cos²(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 x-axis, the final value of cosec 0° is undefined.
☛ Also Check:
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/√(1-cos²(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 x-axis, 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 y-coordinate (0). ∴ cosec 0° = undefined(∞).