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Tan 11pi/6
The value of tan 11pi/6 is 0.5773502. . .. Tan 11pi/6 radians in degrees is written as tan ((11π/6) × 180°/π), i.e., tan (330°). In this article, we will discuss the methods to find the value of tan 11pi/6 with examples.
 Tan 11pi/6: 1/√3
 Tan 11pi/6 in decimal: 0.5773502. . .
 Tan (11pi/6): 0.5773502. . . or 1/√3
 Tan 11pi/6 in degrees: tan (330°)
What is the Value of Tan 11pi/6?
The value of tan 11pi/6 in decimal is 0.577350269. . .. Tan 11pi/6 can also be expressed using the equivalent of the given angle (11pi/6) in degrees (330°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 11pi/6 radians = 11pi/6 × (180°/pi) = 330° or 330 degrees
∴ tan 11pi/6 = tan 11π/6 = tan(330°) = 1/√3 or 0.5773502. . .
Explanation:
For tan 11pi/6, the angle 11pi/6 lies between 3pi/2 and 2pi (Fourth Quadrant). Since tangent function is negative in the fourth quadrant, thus tan 11pi/6 value = 1/√3 or 0.5773502. . .
Since the tangent function is a periodic function, we can represent tan 11pi/6 as, tan 11pi/6 = tan(11pi/6 + n × pi), n ∈ Z.
⇒ tan 11pi/6 = tan 17pi/6 = tan 23pi/6 , and so on.
Note: Since, tangent is an odd function, the value of tan(11pi/6) = tan(11pi/6).
Methods to Find Value of Tan 11pi/6
The tangent function is negative in the 4th quadrant. The value of tan 11pi/6 is given as 0.57735. . .. We can find the value of tan 11pi/6 by:
 Using Trigonometric Functions
 Using Unit Circle
Tan 11pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 11pi/6 as:
 sin(11pi/6)/cos(11pi/6)
 ± sin(11pi/6)/√(1  sin²(11pi/6))
 ± √(1  cos²(11pi/6))/cos(11pi/6)
 ± 1/√(cosec²(11pi/6)  1)
 ± √(sec²(11pi/6)  1)
 1/cot(11pi/6)
Note: Since 11pi/6 lies in the 4th Quadrant, the final value of tan 11pi/6 will be negative.
We can use trigonometric identities to represent tan 11pi/6 as,
 cot(pi/2  11pi/6) = cot(4pi/3)
 cot(pi/2 + 11pi/6) = cot 7pi/3
 tan (pi  11pi/6) = tan(5pi/6)
Tan 11pi/6 Using Unit Circle
To find the value of tan 11π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form 11pi/6 angle with the positive xaxis.
 The tan of 11pi/6 equals the ycoordinate(0.5) divided by the xcoordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of tan 11pi/6 = y/x = 0.5774 (approx)
☛ Also Check:
Examples Using Tan 11pi/6

Example 1: Find the value of tan 11pi/6 if cot 11pi/6 is 1.7320.
Solution:
Since, tan 11pi/6 = 1/cot(11pi/6)
⇒ tan 11pi/6 = 1/(1.7320) = 0.5774 
Example 2: Simplify: 6 (tan(11pi/6)/cot(4pi/3))
Solution:
We know tan 11pi/6 = cot(4pi/3)
⇒ 6 tan(11pi/6)/cot(4pi/3) = 6 tan(11pi/6)/tan(11pi/6)
= 6(1) = 6 
Example 3: Using the value of tan 11pi/6, solve: (sec²(11pi/6)  1).
Solution:
We know, (sec²(11pi/6)  1) = (tan²(11pi/6)) = 0.3333
⇒ (sec²(11pi/6)  1) = 0.3333
FAQs on Tan 11pi/6
What is Tan 11pi/6?
Tan 11pi/6 is the value of tangent trigonometric function for an angle equal to 11π/6 radians. The value of tan 11pi/6 is 1/√3 or 0.5774 (approx).
What is the Value of Tan 11pi/6 in Terms of Sec 11pi/6?
We can represent the tangent function in terms of the secant function using trig identities, tan 11pi/6 can be written as √(sec²(11pi/6)  1). Here, the value of sec 11pi/6 is equal to 1.1547.
How to Find Tan 11pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 11pi/6 can be given in terms of other trigonometric functions as:
 sin(11pi/6)/cos(11pi/6)
 ± sin(11pi/6)/√(1  sin²(11pi/6))
 ± √(1  cos²(11pi/6))/cos(11pi/6)
 ± 1/√(cosec²(11pi/6)  1)
 ± √(sec²(11pi/6)  1)
 1/cot(11pi/6)
☛ Also check: trigonometry table
How to Find the Value of Tan 11pi/6?
The value of tan 11pi/6 can be calculated by constructing an angle of 11π/6 radians with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of tan 11pi/6 is equal to the ycoordinate(0.5) divided by the xcoordinate (0.866). ∴ tan 11pi/6 = 1/√3 or 0.5774
What is the Value of Tan 11pi/6 in Terms of Cot 11pi/6?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 11pi/6 as 1/cot(11pi/6). The value of cot 11pi/6 is equal to √3.
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