Tan pi/12
The value of tan pi/12 is 0.2679491. . .. Tan pi/12 radians in degrees is written as tan ((π/12) × 180°/π), i.e., tan (15°). In this article, we will discuss the methods to find the value of tan pi/12 with examples.
 Tan pi/12: 2  √3
 Tan pi/12 in decimal: 0.2679491. . .
 Tan (pi/12): 0.2679491. . . or 2 + √3
 Tan pi/12 in degrees: tan (15°)
What is the Value of Tan pi/12?
The value of tan pi/12 in decimal is 0.267949192. . .. Tan pi/12 can also be expressed using the equivalent of the given angle (pi/12) in degrees (15°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/12 radians = pi/12 × (180°/pi) = 15° or 15 degrees
∴ tan pi/12 = tan π/12 = tan(15°) = 2  √3 or 0.2679491. . .
Explanation:
For tan pi/12, the angle pi/12 lies between 0 and pi/2 (First Quadrant). Since tangent function is positive in the first quadrant, thus tan pi/12 value = 2  √3 or 0.2679491. . .
Since the tangent function is a periodic function, we can represent tan pi/12 as, tan pi/12 = tan(pi/12 + n × pi), n ∈ Z.
⇒ tan pi/12 = tan 13pi/12 = tan 25pi/12 , and so on.
Note: Since, tangent is an odd function, the value of tan(pi/12) = tan(pi/12).
Methods to Find Value of Tan pi/12
The tangent function is positive in the 1st quadrant. The value of tan pi/12 is given as 0.26794. . .. We can find the value of tan pi/12 by:
 Using Unit Circle
 Using Trigonometric Functions
Tan pi/12 Using Unit Circle
To find the value of tan π/12 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/12 angle with the positive xaxis.
 The tan of pi/12 equals the ycoordinate(0.2588) divided by the xcoordinate(0.9659) of the point of intersection (0.9659, 0.2588) of unit circle and r.
Hence the value of tan pi/12 = y/x = 0.2679 (approx)
Tan pi/12 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan pi/12 as:
 sin(pi/12)/cos(pi/12)
 ± sin(pi/12)/√(1  sin²(pi/12))
 ± √(1  cos²(pi/12))/cos(pi/12)
 ± 1/√(cosec²(pi/12)  1)
 ± √(sec²(pi/12)  1)
 1/cot(pi/12)
Note: Since pi/12 lies in the 1st Quadrant, the final value of tan pi/12 will be positive.
We can use trigonometric identities to represent tan pi/12 as,
 cot(pi/2  pi/12) = cot 5pi/12
 cot(pi/2 + pi/12) = cot 7pi/12
 tan (pi  pi/12) = tan 11pi/12
☛ Also Check:
Examples Using Tan pi/12

Example 1: Find the value of 2 tan(pi/12)/8 tan(11pi/12).
Solution:
Using trigonometric identities, we know, tan(pi/12) = tan(pi  pi/12) = tan 11pi/12.
⇒ tan(pi/12) = tan(11pi/12)
⇒ Value of 2 tan(pi/12)/8 tan(11pi/12) = 2/8 = 1/4 
Example 2: Find the value of 2 tan(pi/24)/(1  tan²(pi/24)). [Hint: Use tan pi/12 = 0.2679]
Solution:
Using the tan 2a formula,
2 tan(pi/24)/(1  tan²(pi/24)) = tan(2 × pi/24) = tan pi/12
∵ tan pi/12 = 0.2679
⇒ 2 tan(pi/24)/(1  tan²(pi/24)) = 0.2679 
Example 3: Simplify: 6 (tan(pi/12)/cot(5pi/12))
Solution:
We know tan pi/12 = cot 5pi/12
⇒ 6 tan(pi/12)/cot(5pi/12) = 6 tan(pi/12)/tan(pi/12)
= 6(1) = 6
FAQs on Tan pi/12
What is Tan pi/12?
Tan pi/12 is the value of tangent trigonometric function for an angle equal to π/12 radians. The value of tan pi/12 is 2  √3 or 0.2679 (approx).
How to Find Tan pi/12 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan pi/12 can be given in terms of other trigonometric functions as:
 sin(pi/12)/cos(pi/12)
 ± sin(pi/12)/√(1  sin²(pi/12))
 ± √(1  cos²(pi/12))/cos(pi/12)
 ± 1/√(cosec²(pi/12)  1)
 ± √(sec²(pi/12)  1)
 1/cot(pi/12)
☛ Also check: trigonometric table
What is the Value of Tan pi/12 in Terms of Sec pi/12?
We can represent the tangent function in terms of the secant function using trig identities, tan pi/12 can be written as √(sec²(pi/12)  1). Here, the value of sec pi/12 is equal to 1.0352.
What is the Value of Tan pi/12 in Terms of Cos pi/12?
We know, using trig identities, we can write tan pi/12 as √(1  cos²(pi/12))/cos pi/12. Here, the value of cos pi/12 is equal to 0.965925.
How to Find the Value of Tan pi/12?
The value of tan pi/12 can be calculated by constructing an angle of π/12 radians with the xaxis, and then finding the coordinates of the corresponding point (0.9659, 0.2588) on the unit circle. The value of tan pi/12 is equal to the ycoordinate(0.2588) divided by the xcoordinate (0.9659). ∴ tan pi/12 = 2  √3 or 0.2679
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