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Tan 7pi/6
The value of tan 7pi/6 is 0.5773502. . .. Tan 7pi/6 radians in degrees is written as tan ((7π/6) × 180°/π), i.e., tan (210°). In this article, we will discuss the methods to find the value of tan 7pi/6 with examples.
 Tan 7pi/6: 1/√3
 Tan 7pi/6 in decimal: 0.5773502. . .
 Tan (7pi/6): 0.5773502. . . or 1/√3
 Tan 7pi/6 in degrees: tan (210°)
What is the Value of Tan 7pi/6?
The value of tan 7pi/6 in decimal is 0.577350269. . .. Tan 7pi/6 can also be expressed using the equivalent of the given angle (7pi/6) in degrees (210°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/6 radians = 7pi/6 × (180°/pi) = 210° or 210 degrees
∴ tan 7pi/6 = tan 7π/6 = tan(210°) = 1/√3 or 0.5773502. . .
Explanation:
For tan 7pi/6, the angle 7pi/6 lies between pi and 3pi/2 (Third Quadrant). Since tangent function is positive in the third quadrant, thus tan 7pi/6 value = 1/√3 or 0.5773502. . .
Since the tangent function is a periodic function, we can represent tan 7pi/6 as, tan 7pi/6 = tan(7pi/6 + n × pi), n ∈ Z.
⇒ tan 7pi/6 = tan 13pi/6 = tan 19pi/6 , and so on.
Note: Since, tangent is an odd function, the value of tan(7pi/6) = tan(7pi/6).
Methods to Find Value of Tan 7pi/6
The tangent function is positive in the 3rd quadrant. The value of tan 7pi/6 is given as 0.57735. . .. We can find the value of tan 7pi/6 by:
 Using Unit Circle
 Using Trigonometric Functions
Tan 7pi/6 Using Unit Circle
To find the value of tan 7π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form 7pi/6 angle with the positive xaxis.
 The tan of 7pi/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 7pi/6 = y/x = 0.5774 (approx)
Tan 7pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 7pi/6 as:
 sin(7pi/6)/cos(7pi/6)
 ± sin(7pi/6)/√(1  sin²(7pi/6))
 ± √(1  cos²(7pi/6))/cos(7pi/6)
 ± 1/√(cosec²(7pi/6)  1)
 ± √(sec²(7pi/6)  1)
 1/cot(7pi/6)
Note: Since 7pi/6 lies in the 3rd Quadrant, the final value of tan 7pi/6 will be positive.
We can use trigonometric identities to represent tan 7pi/6 as,
 cot(pi/2  7pi/6) = cot(2pi/3)
 cot(pi/2 + 7pi/6) = cot 5pi/3
 tan (pi  7pi/6) = tan(pi/6)
☛ Also Check:
Examples Using Tan 7pi/6

Example 1: Using the value of tan 7pi/6, solve: (sec²(7pi/6)  1).
Solution:
We know, (sec²(7pi/6)  1) = (tan²(7pi/6)) = 0.3333
⇒ (sec²(7pi/6)  1) = 0.3333 
Example 2: Simplify: 4 (tan(7pi/6)/cot(2pi/3))
Solution:
We know tan 7pi/6 = cot(2pi/3)
⇒ 4 tan(7pi/6)/cot(2pi/3) = 4 tan(7pi/6)/tan(7pi/6)
= 4(1) = 4 
Example 3: Find the value of (2 sin (7pi/12) cos (7pi/12) sec (7pi/6)). [Hint: Use tan 7pi/6 = 0.5774]
Solution:
Using sin 2a formula,
2 sin (7pi/12) cos (7pi/12) = sin (2 × 7pi/12) = sin 7pi/6
⇒ 2 sin (7pi/12) cos (7pi/12) sec(7pi/6) = sin(7pi/6) sec(7pi/6)
= sin(7pi/6)/cos(7pi/6) = tan 7pi/6
⇒ (2 sin (7pi/12) cos (7pi/12) sec(7pi/6)) = 0.5774
FAQs on Tan 7pi/6
What is Tan 7pi/6?
Tan 7pi/6 is the value of tangent trigonometric function for an angle equal to 7π/6 radians. The value of tan 7pi/6 is 1/√3 or 0.5774 (approx).
How to Find Tan 7pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 7pi/6 can be given in terms of other trigonometric functions as:
 sin(7pi/6)/cos(7pi/6)
 ± sin(7pi/6)/√(1  sin²(7pi/6))
 ± √(1  cos²(7pi/6))/cos(7pi/6)
 ± 1/√(cosec²(7pi/6)  1)
 ± √(sec²(7pi/6)  1)
 1/cot(7pi/6)
☛ Also check: trigonometry table
What is the Value of Tan 7pi/6 in Terms of Cos 7pi/6?
We know, using trig identities, we can write tan 7pi/6 as √(1  cos²(7pi/6))/cos 7pi/6. Here, the value of cos 7pi/6 is equal to 0.866025.
How to Find the Value of Tan 7pi/6?
The value of tan 7pi/6 can be calculated by constructing an angle of 7π/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 7pi/6 is equal to the ycoordinate(0.5) divided by the xcoordinate (0.866). ∴ tan 7pi/6 = 1/√3 or 0.5774
What is the Exact Value of tan 7pi/6?
The exact value of tan 7pi/6 can be given accurately up to 8 decimal places as 0.57735026 or as 1/√3.
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