Cot 7 Degrees
The value of cot 7 degrees is 8.1443464. . .. Cot 7 degrees in radians is written as cot (7° × π/180°), i.e., cot (0.122173. . .). In this article, we will discuss the methods to find the value of cot 7 degrees with examples.
 Cot 7° in decimal: 8.1443464. . .
 Cot (7 degrees): 8.1443464. . .
 Cot 7° in radians: cot (0.1221730 . . .)
What is the Value of Cot 7 Degrees?
The value of cot 7 degrees in decimal is 8.144346427. . .. Cot 7 degrees can also be expressed using the equivalent of the given angle (7 degrees) in radians (0.12217 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 7 degrees = 7° × (π/180°) rad = 0.1221 . . .
∴ cot 7° = cot(0.1221) = 8.1443464. . .
Explanation:
For cot 7 degrees, the angle 7° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 7° value = 8.1443464. . .
Since the cotangent function is a periodic function, we can represent cot 7° as, cot 7 degrees = cot(7° + n × 180°), n ∈ Z.
⇒ cot 7° = cot 187° = cot 367°, and so on.
Note: Since, cotangent is an odd function, the value of cot(7°) = cot(7°).
Methods to Find Value of Cot 7 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 7° is given as 8.14434. . . We can find the value of cot 7 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cot 7° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 7 degrees as:
 cos(7°)/sin(7°)
 ± cos 7°/√(1  cos²(7°))
 ± √(1  sin²(7°))/sin 7°
 ± 1/√(sec²(7°)  1)
 ± √(cosec²(7°)  1)
 1/tan 7°
Note: Since 7° lies in the 1st Quadrant, the final value of cot 7° will be positive.
We can use trigonometric identities to represent cot 7° as,
 tan (90°  7°) = tan 83°
 tan (90° + 7°) = tan 97°
 cot (180°  7°) = cot 173°
Cot 7 Degrees Using Unit Circle
To find the value of cot 7 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 7° angle with the positive xaxis.
 The cot of 7 degrees equals the xcoordinate(0.9925) divided by ycoordinate(0.1219) of the point of intersection (0.9925, 0.1219) of unit circle and r.
Hence the value of cot 7° = x/y = 8.1443 (approx).
☛ Also Check:
Examples Using Cot 7 Degrees

Example 1: Find the value of (cos (7°) cosec (3.5°) sec (3.5°))/2. [Hint: Use cot 7° = 8.1443]
Solution:
Using trigonometry formulas,
(cos (7°) cosec (3.5°) sec (3.5°))/2 = cos (7°)/(2 sin (3.5°) cos (3.5°))
Using sin 2a formula,
2 sin (3.5°) cos (3.5°) = sin (2 × 3.5°) = sin 7°
⇒ cos (7°) / sin (7°) = cot 7°
⇒ (cos (7°) cosec (3.5°) sec (3.5°))/2 = 8.1443 
Example 2: Simplify: 7 (cot 7°/tan 83°)
Solution:
We know cot 7° = tan 83°
⇒ 7 cot 7°/tan 83° = 7 (cot 7°/cot 7°)
= 7(1) = 7 
Example 3: Find the value of cot 7° if tan 7° is 0.1227.
Solution:
Since, cot 7° = 1/tan 7°
⇒ cot 7° = 1/0.1227 = 8.1443
FAQs on Cot 7 Degrees
What is Cot 7 Degrees?
Cot 7 degrees is the value of cotangent trigonometric function for an angle equal to 7 degrees. The value of cot 7° is 8.1443 (approx).
What is the Value of Cot 7° in Terms of Sec 7°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 7° can be written as 1/√(sec²(7°)  1). Here, the value of sec 7° is equal to 1.0075.
How to Find the Value of Cot 7 Degrees?
The value of cot 7 degrees can be calculated by constructing an angle of 7° with the xaxis, and then finding the coordinates of the corresponding point (0.9925, 0.1219) on the unit circle. The value of cot 7° is equal to the xcoordinate(0.9925) divided by the ycoordinate (0.1219). ∴ cot 7° = 8.1443
What is the Value of Cot 7 Degrees in Terms of Tan 7°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 7° as 1/tan(7°). The value of tan 7° is equal to 0.12278.
How to Find Cot 7° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 7° can be given in terms of other trigonometric functions as:
 cos(7°)/sin(7°)
 ± cos 7°/√(1  cos²(7°))
 ± √(1  sin²(7°))/sin 7°
 ± 1/√(sec²(7°)  1)
 ± √(cosec²(7°)  1)
 1/tan 7°
☛ Also check: trigonometric table
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