Cot 5 Degrees
The value of cot 5 degrees is 11.4300523. . .. Cot 5 degrees in radians is written as cot (5° × π/180°), i.e., cot (π/36) or cot (0.087266. . .). In this article, we will discuss the methods to find the value of cot 5 degrees with examples.
- Cot 5° in decimal: 11.4300523. . .
- Cot (-5 degrees): -11.4300523. . .
- Cot 5° in radians: cot (π/36) or cot (0.0872664 . . .)
What is the Value of Cot 5 Degrees?
The value of cot 5 degrees in decimal is 11.430052302. . .. Cot 5 degrees can also be expressed using the equivalent of the given angle (5 degrees) in radians (0.08726 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 5 degrees = 5° × (π/180°) rad = π/36 or 0.0872 . . .
∴ cot 5° = cot(0.0872) = 11.4300523. . .
![cot 5 Degrees](https://static.qumath.in/static/website/old-cdn-static/trigonometry/cot-5.png)
Explanation:
For cot 5 degrees, the angle 5° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 5° value = 11.4300523. . .
Since the cotangent function is a periodic function, we can represent cot 5° as, cot 5 degrees = cot(5° + n × 180°), n ∈ Z.
⇒ cot 5° = cot 185° = cot 365°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-5°) = -cot(5°).
Methods to Find Value of Cot 5 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 5° is given as 11.43005. . . We can find the value of cot 5 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cot 5 Degrees Using Unit Circle
![Value of cot 5](https://static.qumath.in/static/website/old-cdn-static/trigonometry/value-of-cot-5-degrees.png)
To find the value of cot 5 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 5° angle with the positive x-axis.
- The cot of 5 degrees equals the x-coordinate(0.9962) divided by y-coordinate(0.0872) of the point of intersection (0.9962, 0.0872) of unit circle and r.
Hence the value of cot 5° = x/y = 11.4301 (approx).
Cot 5° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 5 degrees as:
- cos(5°)/sin(5°)
- ± cos 5°/√(1 - cos²(5°))
- ± √(1 - sin²(5°))/sin 5°
- ± 1/√(sec²(5°) - 1)
- ± √(cosec²(5°) - 1)
- 1/tan 5°
Note: Since 5° lies in the 1st Quadrant, the final value of cot 5° will be positive.
We can use trigonometric identities to represent cot 5° as,
- tan (90° - 5°) = tan 85°
- -tan (90° + 5°) = -tan 95°
- -cot (180° - 5°) = -cot 175°
☛ Also Check:
Examples Using Cot 5 Degrees
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Example 1: Find the value of 5 cot(5°)/7 cot(175°).
Solution:
Using trigonometric identities, we know, cot(5°) = -cot(180° - 5°) = -cot 175°.
⇒ cot(5°) = -cot(175°)
⇒ Value of 5 cot(5°)/7 cot(175°) = -5/7 -
Example 2: Simplify: 9 (cot 5°/tan 85°)
Solution:
We know cot 5° = tan 85°
⇒ 9 cot 5°/tan 85° = 9 (cot 5°/cot 5°)
= 9(1) = 9 -
Example 3: Using the value of cot 5°, solve: (cosec²(5°) - 1).
Solution:
We know, (cosec²(5°) - 1) = (cot²(5°)) = 130.6461
⇒ (cosec²(5°) - 1) = 130.6461
FAQs on Cot 5 Degrees
What is Cot 5 Degrees?
Cot 5 degrees is the value of cotangent trigonometric function for an angle equal to 5 degrees. The value of cot 5° is 11.4301 (approx).
What is the Value of Cot 5° in Terms of Cosec 5°?
Since the cotangent function can be represented using the cosecant function, we can write cot 5° as √(cosec²(5°) - 1). The value of cosec 5° is equal to 11.47371.
What is the Value of Cot 5 Degrees in Terms of Sin 5°?
Using trigonometric identities, we can write cot 5° in terms of sin 5° as, cot(5°) = √(1 - sin²(5°))/sin 5° . Here, the value of sin 5° is equal to 0.0872.
How to Find Cot 5° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 5° can be given in terms of other trigonometric functions as:
- cos(5°)/sin(5°)
- ± cos 5°/√(1 - cos²(5°))
- ± √(1 - sin²(5°))/sin 5°
- ± 1/√(sec²(5°) - 1)
- ± √(cosec²(5°) - 1)
- 1/tan 5°
☛ Also check: trigonometric table
How to Find the Value of Cot 5 Degrees?
The value of cot 5 degrees can be calculated by constructing an angle of 5° with the x-axis, and then finding the coordinates of the corresponding point (0.9962, 0.0872) on the unit circle. The value of cot 5° is equal to the x-coordinate(0.9962) divided by the y-coordinate (0.0872). ∴ cot 5° = 11.4301
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