Cot 0 Degrees
The value of cot 0 degrees is undefined(∞). Cot 0 degrees in radians is written as cot (0° × π/180°), i.e., cot (0π) or cot (0). In this article, we will discuss the methods to find the value of cot 0 degrees with examples.
- Cot 0°: undefined(∞)
- Cot 0° in radians: cot (0π) or cot (0 . . .)
What is the Value of Cot 0 Degrees?
The value of cot 0 degrees is ∞. Cot 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 . . .
∴ cot 0° = cot(0) = undefined(∞)
Explanation:
For cot 0 degrees, the angle 0° lies on the positive x-axis. Thus, cot 0° value = undefined(∞)
Since the cotangent function is a periodic function, we can represent cot 0° as, cot 0 degrees = cot(0° + n × 180°), n ∈ Z.
⇒ cot 0° = cot 180° = cot 360°, and so on.
Methods to Find Value of Cot 0 Degrees
The value of cot 0° is given as undefined(∞). We can find the value of cot 0 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cot 0 Degrees Using Unit Circle
To find the value of cot 0 degrees using the unit circle:
- Draw the radius of unit circle, ‘r’, to form 0° angle with the positive x-axis.
- The cot of 0 degrees equals the x-coordinate(1) divided by y-coordinate(0) of the point of intersection (1, 0) of unit circle and r.
Hence the value of cot 0° = x/y = undefined(∞).
Cot 0° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 0 degrees as:
- cos(0°)/sin(0°)
- ± cos 0°/√(1 - cos²(0°))
- ± √(1 - sin²(0°))/sin 0°
- ± 1/√(sec²(0°) - 1)
- ± √(cosec²(0°) - 1)
- 1/tan 0°
We can use trigonometric identities to represent cot 0° as,
- tan (90° - 0°) = tan 90°
- -tan (90° + 0°) = -tan 90°
- -cot (180° - 0°) = -cot 180°
Note: Since 0° lies on the positive x-axis, the final value of cot 0° will be undefined(∞).
☛ Also Check:
FAQs on Cot 0 Degrees
What is Cot 0 Degrees?
Cot 0 degrees is the value of cotangent trigonometric function for an angle equal to 0 degrees. The value of cot 0° is not defined or ∞.
What is the Value of Cot 0 Degrees in Terms of Sin 0°?
Using trigonometric identities, we can write cot 0° in terms of sin 0° as, cot(0°) = √(1 - sin²(0°))/sin 0° . Here, the value of sin 0° is equal to 0.
How to Find Cot 0° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 0° can be given in terms of other trigonometric functions as:
- cos(0°)/sin(0°)
- ± cos 0°/√(1 - cos²(0°))
- ± √(1 - sin²(0°))/sin 0°
- ± 1/√(sec²(0°) - 1)
- ± √(cosec²(0°) - 1)
- 1/tan 0°
☛ Also check: trigonometry table
How to Find the Value of Cot 0 Degrees?
The value of cot 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 cot 0° is equal to the x-coordinate(1) divided by the y-coordinate (0). ∴ cot 0° = undefined(∞)
What is the Value of Cot 0° in Terms of Sec 0°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 0° can be written as 1/√(sec²(0°) - 1). Here, the value of sec 0° is equal to 1.