Cot 238 Degrees
The value of cot 238 degrees is 0.6248693. . .. Cot 238 degrees in radians is written as cot (238° × π/180°), i.e., cot (119π/90) or cot (4.153883. . .). In this article, we will discuss the methods to find the value of cot 238 degrees with examples.
- Cot 238° in decimal: 0.6248693. . .
- Cot (-238 degrees): -0.6248693. . .
- Cot 238° in radians: cot (119π/90) or cot (4.1538836 . . .)
What is the Value of Cot 238 Degrees?
The value of cot 238 degrees in decimal is 0.624869351. . .. Cot 238 degrees can also be expressed using the equivalent of the given angle (238 degrees) in radians (4.15388 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 238 degrees = 238° × (π/180°) rad = 119π/90 or 4.1538 . . .
∴ cot 238° = cot(4.1538) = 0.6248693. . .
Explanation:
For cot 238 degrees, the angle 238° lies between 180° and 270° (Third Quadrant). Since cotangent function is positive in the third quadrant, thus cot 238° value = 0.6248693. . .
Since the cotangent function is a periodic function, we can represent cot 238° as, cot 238 degrees = cot(238° + n × 180°), n ∈ Z.
⇒ cot 238° = cot 418° = cot 598°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-238°) = -cot(238°).
Methods to Find Value of Cot 238 Degrees
The cotangent function is positive in the 3rd quadrant. The value of cot 238° is given as 0.62486. . . We can find the value of cot 238 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cot 238 Degrees Using Unit Circle
To find the value of cot 238 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 238° angle with the positive x-axis.
- The cot of 238 degrees equals the x-coordinate(-0.5299) divided by y-coordinate(-0.848) of the point of intersection (-0.5299, -0.848) of unit circle and r.
Hence the value of cot 238° = x/y = 0.6249 (approx).
Cot 238° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 238 degrees as:
- cos(238°)/sin(238°)
- ± cos 238°/√(1 - cos²(238°))
- ± √(1 - sin²(238°))/sin 238°
- ± 1/√(sec²(238°) - 1)
- ± √(cosec²(238°) - 1)
- 1/tan 238°
Note: Since 238° lies in the 3rd Quadrant, the final value of cot 238° will be positive.
We can use trigonometric identities to represent cot 238° as,
- tan (90° - 238°) = tan(-148°)
- -tan (90° + 238°) = -tan 328°
- -cot (180° - 238°) = -cot(-58°)
☛ Also Check:
FAQs on Cot 238 Degrees
What is Cot 238 Degrees?
Cot 238 degrees is the value of cotangent trigonometric function for an angle equal to 238 degrees. The value of cot 238° is 0.6249 (approx).
How to Find the Value of Cot 238 Degrees?
The value of cot 238 degrees can be calculated by constructing an angle of 238° with the x-axis, and then finding the coordinates of the corresponding point (-0.5299, -0.848) on the unit circle. The value of cot 238° is equal to the x-coordinate(-0.5299) divided by the y-coordinate (-0.848). ∴ cot 238° = 0.6249
What is the Value of Cot 238 Degrees in Terms of Tan 238°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 238° as 1/tan(238°). The value of tan 238° is equal to 1.60033.
How to Find Cot 238° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 238° can be given in terms of other trigonometric functions as:
- cos(238°)/sin(238°)
- ± cos 238°/√(1 - cos²(238°))
- ± √(1 - sin²(238°))/sin 238°
- ± 1/√(sec²(238°) - 1)
- ± √(cosec²(238°) - 1)
- 1/tan 238°
☛ Also check: trigonometry table
What is the Exact Value of Cot 238 Degrees?
The exact value of cot 238 degrees can be given accurately up to 8 decimal places as 0.62486935.