Tan 5pi/6
The value of tan 5pi/6 is 0.5773502. . .. Tan 5pi/6 radians in degrees is written as tan ((5π/6) × 180°/π), i.e., tan (150°). In this article, we will discuss the methods to find the value of tan 5pi/6 with examples.
 Tan 5pi/6: 1/√3
 Tan 5pi/6 in decimal: 0.5773502. . .
 Tan (5pi/6): 0.5773502. . . or 1/√3
 Tan 5pi/6 in degrees: tan (150°)
What is the Value of Tan 5pi/6?
The value of tan 5pi/6 in decimal is 0.577350269. . .. Tan 5pi/6 can also be expressed using the equivalent of the given angle (5pi/6) in degrees (150°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/6 radians = 5pi/6 × (180°/pi) = 150° or 150 degrees
∴ tan 5pi/6 = tan 5π/6 = tan(150°) = 1/√3 or 0.5773502. . .
Explanation:
For tan 5pi/6, the angle 5pi/6 lies between pi/2 and pi (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 5pi/6 value = 1/√3 or 0.5773502. . .
Since the tangent function is a periodic function, we can represent tan 5pi/6 as, tan 5pi/6 = tan(5pi/6 + n × pi), n ∈ Z.
⇒ tan 5pi/6 = tan 11pi/6 = tan 17pi/6 , and so on.
Note: Since, tangent is an odd function, the value of tan(5pi/6) = tan(5pi/6).
Methods to Find Value of Tan 5pi/6
The tangent function is negative in the 2nd quadrant. The value of tan 5pi/6 is given as 0.57735. . .. We can find the value of tan 5pi/6 by:
 Using Unit Circle
 Using Trigonometric Functions
Tan 5pi/6 Using Unit Circle
To find the value of tan 5π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form 5pi/6 angle with the positive xaxis.
 The tan of 5pi/6 equals the ycoordinate(0.5) divided by the xcoordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of tan 5pi/6 = y/x = 0.5774 (approx)
Tan 5pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 5pi/6 as:
 sin(5pi/6)/cos(5pi/6)
 ± sin(5pi/6)/√(1  sin²(5pi/6))
 ± √(1  cos²(5pi/6))/cos(5pi/6)
 ± 1/√(cosec²(5pi/6)  1)
 ± √(sec²(5pi/6)  1)
 1/cot(5pi/6)
Note: Since 5pi/6 lies in the 2nd Quadrant, the final value of tan 5pi/6 will be negative.
We can use trigonometric identities to represent tan 5pi/6 as,
 cot(pi/2  5pi/6) = cot(pi/3)
 cot(pi/2 + 5pi/6) = cot 4pi/3
 tan (pi  5pi/6) = tan pi/6
☛ Also Check:
Examples Using Tan 5pi/6

Example 1: Simplify: 3 (tan(5pi/6)/cot(pi/3))
Solution:
We know tan 5pi/6 = cot(pi/3)
⇒ 3 tan(5pi/6)/cot(pi/3) = 3 tan(5pi/6)/tan(5pi/6)
= 3(1) = 3 
Example 2: Find the value of 5 tan(5pi/6)/10 tan(pi/6).
Solution:
Using trigonometric identities, we know, tan(5pi/6) = tan(pi  5pi/6) = tan pi/6.
⇒ tan(5pi/6) = tan(pi/6)
⇒ Value of 5 tan(5pi/6)/10 tan(pi/6) = 5/10 = 1/2 
Example 3: Find the value of 2 tan(5pi/12)/(1  tan²(5pi/12)). [Hint: Use tan 5pi/6 = 0.5774]
Solution:
Using the tan 2a formula,
2 tan(5pi/12)/(1  tan²(5pi/12)) = tan(2 × 5pi/12) = tan 5pi/6
∵ tan 5pi/6 = 0.5774
⇒ 2 tan(5pi/12)/(1  tan²(5pi/12)) = 0.5774
FAQs on Tan 5pi/6
What is Tan 5pi/6?
Tan 5pi/6 is the value of tangent trigonometric function for an angle equal to 5π/6 radians. The value of tan 5pi/6 is 1/√3 or 0.5774 (approx).
How to Find the Value of Tan 5pi/6?
The value of tan 5pi/6 can be calculated by constructing an angle of 5π/6 radians with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of tan 5pi/6 is equal to the ycoordinate(0.5) divided by the xcoordinate (0.866). ∴ tan 5pi/6 = 1/√3 or 0.5774
What is the Value of Tan 5pi/6 in Terms of Sec 5pi/6?
We can represent the tangent function in terms of the secant function using trig identities, tan 5pi/6 can be written as √(sec²(5pi/6)  1). Here, the value of sec 5pi/6 is equal to 1.1547.
What is the Value of Tan 5pi/6 in Terms of Sin 5pi/6?
Using trigonometric identities, we can write tan 5pi/6 in terms of sin 5pi/6 as, tan(5pi/6) = sin(5pi/6)/√(1  sin²(5pi/6)) . Here, the value of sin 5pi/6 is equal to 1/2.
How to Find Tan 5pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 5pi/6 can be given in terms of other trigonometric functions as:
 sin(5pi/6)/cos(5pi/6)
 ± sin(5pi/6)/√(1  sin²(5pi/6))
 ± √(1  cos²(5pi/6))/cos(5pi/6)
 ± 1/√(cosec²(5pi/6)  1)
 ± √(sec²(5pi/6)  1)
 1/cot(5pi/6)
☛ Also check: trigonometry table
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