Cot 34 Degrees
The value of cot 34 degrees is 1.4825609. . .. Cot 34 degrees in radians is written as cot (34° × π/180°), i.e., cot (17π/90) or cot (0.593411. . .). In this article, we will discuss the methods to find the value of cot 34 degrees with examples.
- Cot 34° in decimal: 1.4825609. . .
- Cot (-34 degrees): -1.4825609. . .
- Cot 34° in radians: cot (17π/90) or cot (0.5934119 . . .)
What is the Value of Cot 34 Degrees?
The value of cot 34 degrees in decimal is 1.482560968. . .. Cot 34 degrees can also be expressed using the equivalent of the given angle (34 degrees) in radians (0.59341 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 34 degrees = 34° × (π/180°) rad = 17π/90 or 0.5934 . . .
∴ cot 34° = cot(0.5934) = 1.4825609. . .
Explanation:
For cot 34 degrees, the angle 34° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 34° value = 1.4825609. . .
Since the cotangent function is a periodic function, we can represent cot 34° as, cot 34 degrees = cot(34° + n × 180°), n ∈ Z.
⇒ cot 34° = cot 214° = cot 394°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-34°) = -cot(34°).
Methods to Find Value of Cot 34 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 34° is given as 1.48256. . . We can find the value of cot 34 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cot 34° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 34 degrees as:
- cos(34°)/sin(34°)
- ± cos 34°/√(1 - cos²(34°))
- ± √(1 - sin²(34°))/sin 34°
- ± 1/√(sec²(34°) - 1)
- ± √(cosec²(34°) - 1)
- 1/tan 34°
Note: Since 34° lies in the 1st Quadrant, the final value of cot 34° will be positive.
We can use trigonometric identities to represent cot 34° as,
- tan (90° - 34°) = tan 56°
- -tan (90° + 34°) = -tan 124°
- -cot (180° - 34°) = -cot 146°
Cot 34 Degrees Using Unit Circle
To find the value of cot 34 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 34° angle with the positive x-axis.
- The cot of 34 degrees equals the x-coordinate(0.829) divided by y-coordinate(0.5592) of the point of intersection (0.829, 0.5592) of unit circle and r.
Hence the value of cot 34° = x/y = 1.4826 (approx).
☛ Also Check:
FAQs on Cot 34 Degrees
What is Cot 34 Degrees?
Cot 34 degrees is the value of cotangent trigonometric function for an angle equal to 34 degrees. The value of cot 34° is 1.4826 (approx).
How to Find Cot 34° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 34° can be given in terms of other trigonometric functions as:
- cos(34°)/sin(34°)
- ± cos 34°/√(1 - cos²(34°))
- ± √(1 - sin²(34°))/sin 34°
- ± 1/√(sec²(34°) - 1)
- ± √(cosec²(34°) - 1)
- 1/tan 34°
☛ Also check: trigonometry table
What is the Value of Cot 34 Degrees in Terms of Sin 34°?
Using trigonometric identities, we can write cot 34° in terms of sin 34° as, cot(34°) = √(1 - sin²(34°))/sin 34° . Here, the value of sin 34° is equal to 0.5592.
How to Find the Value of Cot 34 Degrees?
The value of cot 34 degrees can be calculated by constructing an angle of 34° with the x-axis, and then finding the coordinates of the corresponding point (0.829, 0.5592) on the unit circle. The value of cot 34° is equal to the x-coordinate(0.829) divided by the y-coordinate (0.5592). ∴ cot 34° = 1.4826
What is the Value of Cot 34° in Terms of Sec 34°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 34° can be written as 1/√(sec²(34°) - 1). Here, the value of sec 34° is equal to 1.2062.