Tan 13pi/12
The value of tan 13pi/12 is 0.2679491. . .. Tan 13pi/12 radians in degrees is written as tan ((13π/12) × 180°/π), i.e., tan (195°). In this article, we will discuss the methods to find the value of tan 13pi/12 with examples.
 Tan 13pi/12: 2  √3
 Tan 13pi/12 in decimal: 0.2679491. . .
 Tan (13pi/12): 0.2679491. . . or 2 + √3
 Tan 13pi/12 in degrees: tan (195°)
What is the Value of Tan 13pi/12?
The value of tan 13pi/12 in decimal is 0.267949192. . .. Tan 13pi/12 can also be expressed using the equivalent of the given angle (13pi/12) in degrees (195°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 13pi/12 radians = 13pi/12 × (180°/pi) = 195° or 195 degrees
∴ tan 13pi/12 = tan 13π/12 = tan(195°) = 2  √3 or 0.2679491. . .
Explanation:
For tan 13pi/12, the angle 13pi/12 lies between pi and 3pi/2 (Third Quadrant). Since tangent function is positive in the third quadrant, thus tan 13pi/12 value = 2  √3 or 0.2679491. . .
Since the tangent function is a periodic function, we can represent tan 13pi/12 as, tan 13pi/12 = tan(13pi/12 + n × pi), n ∈ Z.
⇒ tan 13pi/12 = tan 25pi/12 = tan 37pi/12 , and so on.
Note: Since, tangent is an odd function, the value of tan(13pi/12) = tan(13pi/12).
Methods to Find Value of Tan 13pi/12
The tangent function is positive in the 3rd quadrant. The value of tan 13pi/12 is given as 0.26794. . .. We can find the value of tan 13pi/12 by:
 Using Trigonometric Functions
 Using Unit Circle
Tan 13pi/12 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 13pi/12 as:
 sin(13pi/12)/cos(13pi/12)
 ± sin(13pi/12)/√(1  sin²(13pi/12))
 ± √(1  cos²(13pi/12))/cos(13pi/12)
 ± 1/√(cosec²(13pi/12)  1)
 ± √(sec²(13pi/12)  1)
 1/cot(13pi/12)
Note: Since 13pi/12 lies in the 3rd Quadrant, the final value of tan 13pi/12 will be positive.
We can use trigonometric identities to represent tan 13pi/12 as,
 cot(pi/2  13pi/12) = cot(7pi/12)
 cot(pi/2 + 13pi/12) = cot 19pi/12
 tan (pi  13pi/12) = tan(pi/12)
Tan 13pi/12 Using Unit Circle
To find the value of tan 13π/12 using the unit circle:
 Rotate ‘r’ anticlockwise to form 13pi/12 angle with the positive xaxis.
 The tan of 13pi/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 13pi/12 = y/x = 0.2679 (approx)
☛ Also Check:
Examples Using Tan 13pi/12

Example 1: Find the value of tan 13pi/12 if cot 13pi/12 is 3.7320.
Solution:
Since, tan 13pi/12 = 1/cot(13pi/12)
⇒ tan 13pi/12 = 1/3.7320 = 0.2679 
Example 2: Find the value of 4 tan(13pi/12)/5 tan(pi/12).
Solution:
Using trigonometric identities, we know, tan(13pi/12) = tan(pi  13pi/12) = tan(pi/12).
⇒ tan(13pi/12) = tan(pi/12)
⇒ Value of 4 tan(13pi/12)/5 tan(pi/12) = 4/5 
Example 3: Find the value of (2 sin (13pi/24) cos (13pi/24) sec (13pi/12)). [Hint: Use tan 13pi/12 = 0.2679]
Solution:
Using sin 2a formula,
2 sin (13pi/24) cos (13pi/24) = sin (2 × 13pi/24) = sin 13pi/12
⇒ 2 sin (13pi/24) cos (13pi/24) sec(13pi/12) = sin(13pi/12) sec(13pi/12)
= sin(13pi/12)/cos(13pi/12) = tan 13pi/12
⇒ (2 sin (13pi/24) cos (13pi/24) sec(13pi/12)) = 0.2679
FAQs on Tan 13pi/12
What is Tan 13pi/12?
Tan 13pi/12 is the value of tangent trigonometric function for an angle equal to 13π/12 radians. The value of tan 13pi/12 is 2  √3 or 0.2679 (approx).
What is the Value of Tan 13pi/12 in Terms of Cot 13pi/12?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 13pi/12 as 1/cot(13pi/12). The value of cot 13pi/12 is equal to 2 + √3.
What is the Exact Value of tan 13pi/12?
The exact value of tan 13pi/12 can be given accurately up to 8 decimal places as 0.26794919 or as 2  √3.
How to Find Tan 13pi/12 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 13pi/12 can be given in terms of other trigonometric functions as:
 sin(13pi/12)/cos(13pi/12)
 ± sin(13pi/12)/√(1  sin²(13pi/12))
 ± √(1  cos²(13pi/12))/cos(13pi/12)
 ± 1/√(cosec²(13pi/12)  1)
 ± √(sec²(13pi/12)  1)
 1/cot(13pi/12)
☛ Also check: trigonometric table
How to Find the Value of Tan 13pi/12?
The value of tan 13pi/12 can be calculated by constructing an angle of 13π/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 13pi/12 is equal to the ycoordinate(0.2588) divided by the xcoordinate (0.9659). ∴ tan 13pi/12 = 2  √3 or 0.2679
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