Tan 5pi/3
The value of tan 5pi/3 is 1.7320508. . .. Tan 5pi/3 radians in degrees is written as tan ((5π/3) × 180°/π), i.e., tan (300°). In this article, we will discuss the methods to find the value of tan 5pi/3 with examples.
 Tan 5pi/3: √3
 Tan 5pi/3 in decimal: 1.7320508. . .
 Tan (5pi/3): 1.7320508. . . or √3
 Tan 5pi/3 in degrees: tan (300°)
What is the Value of Tan 5pi/3?
The value of tan 5pi/3 in decimal is 1.732050807. . .. Tan 5pi/3 can also be expressed using the equivalent of the given angle (5pi/3) in degrees (300°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/3 radians = 5pi/3 × (180°/pi) = 300° or 300 degrees
∴ tan 5pi/3 = tan 5π/3 = tan(300°) = √3 or 1.7320508. . .
Explanation:
For tan 5pi/3, the angle 5pi/3 lies between 3pi/2 and 2pi (Fourth Quadrant). Since tangent function is negative in the fourth quadrant, thus tan 5pi/3 value = √3 or 1.7320508. . .
Since the tangent function is a periodic function, we can represent tan 5pi/3 as, tan 5pi/3 = tan(5pi/3 + n × pi), n ∈ Z.
⇒ tan 5pi/3 = tan 8pi/3 = tan 11pi/3 , and so on.
Note: Since, tangent is an odd function, the value of tan(5pi/3) = tan(5pi/3).
Methods to Find Value of Tan 5pi/3
The tangent function is negative in the 4th quadrant. The value of tan 5pi/3 is given as 1.73205. . .. We can find the value of tan 5pi/3 by:
 Using Trigonometric Functions
 Using Unit Circle
Tan 5pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 5pi/3 as:
 sin(5pi/3)/cos(5pi/3)
 ± sin(5pi/3)/√(1  sin²(5pi/3))
 ± √(1  cos²(5pi/3))/cos(5pi/3)
 ± 1/√(cosec²(5pi/3)  1)
 ± √(sec²(5pi/3)  1)
 1/cot(5pi/3)
Note: Since 5pi/3 lies in the 4th Quadrant, the final value of tan 5pi/3 will be negative.
We can use trigonometric identities to represent tan 5pi/3 as,
 cot(pi/2  5pi/3) = cot(7pi/6)
 cot(pi/2 + 5pi/3) = cot 13pi/6
 tan (pi  5pi/3) = tan(2pi/3)
Tan 5pi/3 Using Unit Circle
To find the value of tan 5π/3 using the unit circle:
 Rotate ‘r’ anticlockwise to form 5pi/3 angle with the positive xaxis.
 The tan of 5pi/3 equals the ycoordinate(0.866) divided by the xcoordinate(0.5) of the point of intersection (0.5, 0.866) of unit circle and r.
Hence the value of tan 5pi/3 = y/x = 1.7321 (approx)
☛ Also Check:
Examples Using Tan 5pi/3

Example 1: Simplify: 5 (tan(5pi/3)/cot(7pi/6))
Solution:
We know tan 5pi/3 = cot(7pi/6)
⇒ 5 tan(5pi/3)/cot(7pi/6) = 5 tan(5pi/3)/tan(5pi/3)
= 5(1) = 5 
Example 2: Find the value of 2 tan(5pi/3)/4 tan(2pi/3).
Solution:
Using trigonometric identities, we know, tan(5pi/3) = tan(pi  5pi/3) = tan(2pi/3).
⇒ tan(5pi/3) = tan(2pi/3)
⇒ Value of 2 tan(5pi/3)/4 tan(2pi/3) = 2/4 = 1/2 
Example 3: Find the value of tan 5pi/3 if cot 5pi/3 is 0.5773.
Solution:
Since, tan 5pi/3 = 1/cot(5pi/3)
⇒ tan 5pi/3 = 1/(0.5773) = 1.7321
FAQs on Tan 5pi/3
What is Tan 5pi/3?
Tan 5pi/3 is the value of tangent trigonometric function for an angle equal to 5π/3 radians. The value of tan 5pi/3 is √3 or 1.7321 (approx).
What is the Value of Tan 5pi/3 in Terms of Cosec 5pi/3?
Since the tangent function can be represented using the cosecant function, we can write tan 5pi/3 as 1/√(cosec²(5pi/3)  1). The value of cosec 5pi/3 is equal to 1.15470.
How to Find the Value of Tan 5pi/3?
The value of tan 5pi/3 can be calculated by constructing an angle of 5π/3 radians with the xaxis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of tan 5pi/3 is equal to the ycoordinate(0.866) divided by the xcoordinate (0.5). ∴ tan 5pi/3 = √3 or 1.7321
What is the Value of Tan 5pi/3 in Terms of Sin 5pi/3?
Using trigonometric identities, we can write tan 5pi/3 in terms of sin 5pi/3 as, tan(5pi/3) = sin(5pi/3)/√(1  sin²(5pi/3)) . Here, the value of sin 5pi/3 is equal to (√3/2).
How to Find Tan 5pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 5pi/3 can be given in terms of other trigonometric functions as:
 sin(5pi/3)/cos(5pi/3)
 ± sin(5pi/3)/√(1  sin²(5pi/3))
 ± √(1  cos²(5pi/3))/cos(5pi/3)
 ± 1/√(cosec²(5pi/3)  1)
 ± √(sec²(5pi/3)  1)
 1/cot(5pi/3)
☛ Also check: trigonometry table
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