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Tan pi/6
The value of tan pi/6 is 0.5773502. . .. Tan pi/6 radians in degrees is written as tan ((π/6) × 180°/π), i.e., tan (30°). In this article, we will discuss the methods to find the value of tan pi/6 with examples.
 Tan pi/6: 1/√3
 Tan pi/6 in decimal: 0.5773502. . .
 Tan (pi/6): 0.5773502. . . or 1/√3
 Tan pi/6 in degrees: tan (30°)
What is the Value of Tan pi/6?
The value of tan pi/6 in decimal is 0.577350269. . .. Tan pi/6 can also be expressed using the equivalent of the given angle (pi/6) in degrees (30°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/6 radians = pi/6 × (180°/pi) = 30° or 30 degrees
∴ tan pi/6 = tan π/6 = tan(30°) = 1/√3 or 0.5773502. . .
Explanation:
For tan pi/6, the angle pi/6 lies between 0 and pi/2 (First Quadrant). Since tangent function is positive in the first quadrant, thus tan pi/6 value = 1/√3 or 0.5773502. . .
Since the tangent function is a periodic function, we can represent tan pi/6 as, tan pi/6 = tan(pi/6 + n × pi), n ∈ Z.
⇒ tan pi/6 = tan 7pi/6 = tan 13pi/6 , and so on.
Note: Since, tangent is an odd function, the value of tan(pi/6) = tan(pi/6).
Methods to Find Value of Tan pi/6
The tangent function is positive in the 1st quadrant. The value of tan pi/6 is given as 0.57735. . .. We can find the value of tan pi/6 by:
 Using Unit Circle
 Using Trigonometric Functions
Tan pi/6 Using Unit Circle
To find the value of tan π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/6 angle with the positive xaxis.
 The tan of pi/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 pi/6 = y/x = 0.5774 (approx)
Tan pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan pi/6 as:
 sin(pi/6)/cos(pi/6)
 ± sin(pi/6)/√(1  sin²(pi/6))
 ± √(1  cos²(pi/6))/cos(pi/6)
 ± 1/√(cosec²(pi/6)  1)
 ± √(sec²(pi/6)  1)
 1/cot(pi/6)
Note: Since pi/6 lies in the 1st Quadrant, the final value of tan pi/6 will be positive.
We can use trigonometric identities to represent tan pi/6 as,
 cot(pi/2  pi/6) = cot pi/3
 cot(pi/2 + pi/6) = cot 2pi/3
 tan (pi  pi/6) = tan 5pi/6
☛ Also Check:
Examples Using Tan pi/6

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