Tan 7pi/6

The value of tan 7pi/6 is 0.5773502. . .. Tan 7pi/6 radians in degrees is written as tan ((7π/6) × 180°/π), i.e., tan (210°). In this article, we will discuss the methods to find the value of tan 7pi/6 with examples.

• Tan 7pi/6: 1/√3
• Tan 7pi/6 in decimal: 0.5773502. . .
• Tan (-7pi/6): -0.5773502. . . or -1/√3
• Tan 7pi/6 in degrees: tan (210°)

What is the Value of Tan 7pi/6?

The value of tan 7pi/6 in decimal is 0.577350269. . .. Tan 7pi/6 can also be expressed using the equivalent of the given angle (7pi/6) in degrees (210°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/6 radians = 7pi/6 × (180°/pi) = 210° or 210 degrees
∴ tan 7pi/6 = tan 7π/6 = tan(210°) = 1/√3 or 0.5773502. . .

Explanation:

For tan 7pi/6, the angle 7pi/6 lies between pi and 3pi/2 (Third Quadrant). Since tangent function is positive in the third quadrant, thus tan 7pi/6 value = 1/√3 or 0.5773502. . .
Since the tangent function is a periodic function, we can represent tan 7pi/6 as, tan 7pi/6 = tan(7pi/6 + n × pi), n ∈ Z.
⇒ tan 7pi/6 = tan 13pi/6 = tan 19pi/6 , and so on.
Note: Since, tangent is an odd function, the value of tan(-7pi/6) = -tan(7pi/6).

Methods to Find Value of Tan 7pi/6

The tangent function is positive in the 3rd quadrant. The value of tan 7pi/6 is given as 0.57735. . .. We can find the value of tan 7pi/6 by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 7pi/6 Using Unit Circle

To find the value of tan 7π/6 using the unit circle:

• Rotate ‘r’ anticlockwise to form 7pi/6 angle with the positive x-axis.
• The tan of 7pi/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 7pi/6 = y/x = 0.5774 (approx)

Tan 7pi/6 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 7pi/6 as:

• sin(7pi/6)/cos(7pi/6)
• ± sin(7pi/6)/√(1 - sin²(7pi/6))
• ± √(1 - cos²(7pi/6))/cos(7pi/6)
• ± 1/√(cosec²(7pi/6) - 1)
• ± √(sec²(7pi/6) - 1)
• 1/cot(7pi/6)

Note: Since 7pi/6 lies in the 3rd Quadrant, the final value of tan 7pi/6 will be positive.

We can use trigonometric identities to represent tan 7pi/6 as,

• cot(pi/2 - 7pi/6) = cot(-2pi/3)
• -cot(pi/2 + 7pi/6) = -cot 5pi/3
• -tan (pi - 7pi/6) = -tan(-pi/6)

☛ Also Check:

• sin 5pi/4
• cos 9pi/2
• cos pi/4
• cos 2pi/8
• sin 5pi
• cot 2pi/3

FAQs on Tan 7pi/6

What is Tan 7pi/6?

Tan 7pi/6 is the value of tangent trigonometric function for an angle equal to 7π/6 radians. The value of tan 7pi/6 is 1/√3 or 0.5774 (approx).

How to Find Tan 7pi/6 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 7pi/6 can be given in terms of other trigonometric functions as:

• sin(7pi/6)/cos(7pi/6)
• ± sin(7pi/6)/√(1 - sin²(7pi/6))
• ± √(1 - cos²(7pi/6))/cos(7pi/6)
• ± 1/√(cosec²(7pi/6) - 1)
• ± √(sec²(7pi/6) - 1)
• 1/cot(7pi/6)

☛ Also check: trigonometry table

What is the Value of Tan 7pi/6 in Terms of Cos 7pi/6?

We know, using trig identities, we can write tan 7pi/6 as -√(1 - cos²(7pi/6))/cos 7pi/6. Here, the value of cos 7pi/6 is equal to -0.866025.

How to Find the Value of Tan 7pi/6?

The value of tan 7pi/6 can be calculated by constructing an angle of 7π/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 7pi/6 is equal to the y-coordinate(-0.5) divided by the x-coordinate (-0.866). ∴ tan 7pi/6 = 1/√3 or 0.5774

What is the Exact Value of tan 7pi/6?

The exact value of tan 7pi/6 can be given accurately up to 8 decimal places as 0.57735026 or as 1/√3.