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 x-axis.
• The tan of pi/6 equals the y-coordinate(0.5) divided by the x-coordinate(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:

• tan 5pi/2
• cot pi/6
• csc pi/6
• cot 5pi/6
• cos 3pi/4
• csc pi/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 x-axis, 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 y-coordinate(0.5) divided by the x-coordinate (0.866). ∴ tan pi/6 = 1/√3 or 0.5774