Cot 390 Degrees
The value of cot 390 degrees is 1.7320508. . .. Cot 390 degrees in radians is written as cot (390° × π/180°), i.e., cot (13π/6) or cot (6.806784. . .). In this article, we will discuss the methods to find the value of cot 390 degrees with examples.
 Cot 390°: √3
 Cot 390° in decimal: 1.7320508. . .
 Cot (390 degrees): 1.7320508. . . or √3
 Cot 390° in radians: cot (13π/6) or cot (6.8067840 . . .)
What is the Value of Cot 390 Degrees?
The value of cot 390 degrees in decimal is 1.732050807. . .. Cot 390 degrees can also be expressed using the equivalent of the given angle (390 degrees) in radians (6.80678 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 390 degrees = 390° × (π/180°) rad = 13π/6 or 6.8067 . . .
∴ cot 390° = cot(6.8067) = √3 or 1.7320508. . .
Explanation:
For cot 390°, the angle 390° > 360°. We can represent cot 390° as, cot(390° mod 360°) = cot(30°). The angle 390°, coterminal to angle 30°, is located in the First Quadrant(Quadrant I).
Since cotangent function is positive in the 1st quadrant, thus cot 390 degrees value = √3 or 1.7320508. . .
Similarly, given the periodic property of cot 390°, it can also be written as, cot 390 degrees = (390° + n × 180°), n ∈ Z.
⇒ cot 390° = cot 570° = cot 750°, and so on.
Note: Since, cotangent is an odd function, the value of cot(390°) = cot(390°).
Methods to Find Value of Cot 390 Degrees
The cotangent function is positive in the 1st quadrant. The value of cot 390° is given as 1.73205. . . We can find the value of cot 390 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 390 Degrees Using Unit Circle
To find the value of cot 390 degrees using the unit circle, represent 390° in the form (1 × 360°) + 30° [∵ 390°>360°] ∵ The angle 390° is coterminal to 30° angle and also cotangent is a periodic function, cot 390° = cot 30°.
 Rotate ‘r’ anticlockwise to form 30° or 390° angle with the positive xaxis.
 The cot of 390 degrees equals the xcoordinate(0.866) divided by ycoordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of cot 390° = x/y = 1.7321 (approx).
Cot 390° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 390 degrees as:
 cos(390°)/sin(390°)
 ± cos 390°/√(1  cos²(390°))
 ± √(1  sin²(390°))/sin 390°
 ± 1/√(sec²(390°)  1)
 ± √(cosec²(390°)  1)
 1/tan 390°
Note: Since 390° lies in the 1st Quadrant, the final value of cot 390° will be positive.
We can use trigonometric identities to represent cot 390° as,
 tan (90°  390°) = tan(300°)
 tan (90° + 390°) = tan 480°
 cot (180°  390°) = cot(210°)
☛ Also Check:
Examples Using Cot 390 Degrees

Example 1: Simplify: 7 (cot 390°/tan(300°))
Solution:
We know cot 390° = tan(300°)
⇒ 7 cot 390°/tan(300°) = 7 (cot 390°/cot 390°)
= 7(1) = 7 
Example 2: Find the value of cot 390° if tan 390° is 0.5773.
Solution:
Since, cot 390° = 1/tan 390°
⇒ cot 390° = 1/0.5773 = 1.7321 
Example 3: Find the value of (cos (390°) cosec (195°) sec (195°))/2. [Hint: Use cot 390° = 1.7321]
Solution:
Using trigonometry formulas,
(cos (390°) cosec (195°) sec (195°))/2 = cos (390°)/(2 sin (195°) cos (195°))
Using sin 2a formula,
2 sin (195°) cos (195°) = sin (2 × 195°) = sin 390°
⇒ cos (390°) / sin (390°) = cot 390°
⇒ (cos (390°) cosec (195°) sec (195°))/2 = 1.7321
FAQs on Cot 390 Degrees
What is Cot 390 Degrees?
Cot 390 degrees is the value of cotangent trigonometric function for an angle equal to 390 degrees. The value of cot 390° is √3 or 1.7321 (approx).
How to Find Cot 390° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 390° can be given in terms of other trigonometric functions as:
 cos(390°)/sin(390°)
 ± cos 390°/√(1  cos²(390°))
 ± √(1  sin²(390°))/sin 390°
 ± 1/√(sec²(390°)  1)
 ± √(cosec²(390°)  1)
 1/tan 390°
☛ Also check: trigonometry table
How to Find the Value of Cot 390 Degrees?
The value of cot 390 degrees can be calculated by constructing an angle of 390° with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cot 390° is equal to the xcoordinate(0.866) divided by the ycoordinate (0.5). ∴ cot 390° = 1.7321
What is the Exact Value of Cot 390 Degrees?
The exact value of cot 390 degrees can be given accurately up to 8 decimal places as 1.73205080 or as √3.
What is the Value of Cot 390 Degrees in Terms of Tan 390°?
Since the cotangent function is the reciprocal of the tangent function, we can write cot 390° as 1/tan(390°). The value of tan 390° is equal to 1/√3.
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