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 x-axis.
• The cot of 7 degrees equals the x-coordinate(0.9925) divided by y-coordinate(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:

• cot 390 degrees
• cot 225 degrees
• cot 25 degrees
• cot 116 degrees
• cot 0 degrees
• cot 450 degrees

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 x-axis, 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 x-coordinate(0.9925) divided by the y-coordinate (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