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 x-axis.
• The tan of 13pi/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 13pi/12 = y/x = 0.2679 (approx)

☛ Also Check:

• tan 4pi/3
• cos 17pi/12
• sin 2pi/3
• tan 5pi/4
• sin 7pi/12
• cot 5pi/4

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 x-axis, 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 y-coordinate(-0.2588) divided by the x-coordinate (-0.9659). ∴ tan 13pi/12 = 2 - √3 or 0.2679