Cot 13 Degrees
The value of cot 13 degrees is 4.3314758. . .. Cot 13 degrees in radians is written as cot (13° × π/180°), i.e., cot (0.226892. . .). In this article, we will discuss the methods to find the value of cot 13 degrees with examples.
- Cot 13° in decimal: 4.3314758. . .
- Cot (-13 degrees): -4.3314758. . .
- Cot 13° in radians: cot (0.2268928 . . .)
What is the Value of Cot 13 Degrees?
The value of cot 13 degrees in decimal is 4.331475874. . .. Cot 13 degrees can also be expressed using the equivalent of the given angle (13 degrees) in radians (0.22689 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 13 degrees = 13° × (π/180°) rad = 0.2268 . . .
∴ cot 13° = cot(0.2268) = 4.3314758. . .
Explanation:
For cot 13 degrees, the angle 13° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 13° value = 4.3314758. . .
Since the cotangent function is a periodic function, we can represent cot 13° as, cot 13 degrees = cot(13° + n × 180°), n ∈ Z.
⇒ cot 13° = cot 193° = cot 373°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-13°) = -cot(13°).
Methods to Find Value of Cot 13 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 13° is given as 4.33147. . . We can find the value of cot 13 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cot 13 Degrees Using Unit Circle
To find the value of cot 13 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 13° angle with the positive x-axis.
- The cot of 13 degrees equals the x-coordinate(0.9744) divided by y-coordinate(0.225) of the point of intersection (0.9744, 0.225) of unit circle and r.
Hence the value of cot 13° = x/y = 4.3315 (approx).
Cot 13° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 13 degrees as:
- cos(13°)/sin(13°)
- ± cos 13°/√(1 - cos²(13°))
- ± √(1 - sin²(13°))/sin 13°
- ± 1/√(sec²(13°) - 1)
- ± √(cosec²(13°) - 1)
- 1/tan 13°
Note: Since 13° lies in the 1st Quadrant, the final value of cot 13° will be positive.
We can use trigonometric identities to represent cot 13° as,
- tan (90° - 13°) = tan 77°
- -tan (90° + 13°) = -tan 103°
- -cot (180° - 13°) = -cot 167°
☛ Also Check:
FAQs on Cot 13 Degrees
What is Cot 13 Degrees?
Cot 13 degrees is the value of cotangent trigonometric function for an angle equal to 13 degrees. The value of cot 13° is 4.3315 (approx).
How to Find the Value of Cot 13 Degrees?
The value of cot 13 degrees can be calculated by constructing an angle of 13° with the x-axis, and then finding the coordinates of the corresponding point (0.9744, 0.225) on the unit circle. The value of cot 13° is equal to the x-coordinate(0.9744) divided by the y-coordinate (0.225). ∴ cot 13° = 4.3315
What is the Value of Cot 13 Degrees in Terms of Cos 13°?
We know, using trig identities, we can write cot 13° as cos 13°/√(1 - cos²(13°)). Here, the value of cos 13° is equal to 0.974370.
How to Find Cot 13° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 13° can be given in terms of other trigonometric functions as:
- cos(13°)/sin(13°)
- ± cos 13°/√(1 - cos²(13°))
- ± √(1 - sin²(13°))/sin 13°
- ± 1/√(sec²(13°) - 1)
- ± √(cosec²(13°) - 1)
- 1/tan 13°
☛ Also check: trigonometric table
What is the Value of Cot 13° in Terms of Sec 13°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 13° can be written as 1/√(sec²(13°) - 1). Here, the value of sec 13° is equal to 1.0263.