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 x-axis.
• The tan of pi/12 equals the y-coordinate(0.2588) divided by the x-coordinate(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:

• csc pi/4
• cos pi/3
• tan 5pi/2
• sin pi/2
• cos 3pi/2
• cos 3pi

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 x-axis, 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 y-coordinate(0.2588) divided by the x-coordinate (0.9659). ∴ tan pi/12 = 2 - √3 or 0.2679