Tan 19pi/3
The value of tan 19pi/3 is 1.7320508. . .. Tan 19pi/3 radians in degrees is written as tan ((19π/3) × 180°/π), i.e., tan (1140°). In this article, we will discuss the methods to find the value of tan 19pi/3 with examples.
 Tan 19pi/3: √3
 Tan 19pi/3 in decimal: 1.7320508. . .
 Tan (19pi/3): 1.7320508. . . or √3
 Tan 19pi/3 in degrees: tan (1140°)
What is the Value of Tan 19pi/3?
The value of tan 19pi/3 in decimal is 1.732050807. . .. Tan 19pi/3 can also be expressed using the equivalent of the given angle (19pi/3) in degrees (1140°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 19pi/3 radians = 19pi/3 × (180°/pi) = 1140° or 1140 degrees
∴ tan 19pi/3 = tan 19π/3 = tan(1140°) = √3 or 1.7320508. . .
Explanation:
For tan 19pi/3, the angle 19pi/3 > 2pi. We can represent tan 19pi/3 as, tan(19pi/3 mod 2pi) = tan(pi/3). The angle 19pi/3, coterminal to angle pi/3, is located in the First Quadrant(Quadrant I).
Since tan function is positive in the 1st quadrant, thus tan 19pi/3 value = √3 or 1.7320508. . .
Similarly, given the periodic property of tan 19pi/3, it can also be written as, tan 19pi/3 = (19pi/3 + n × pi), n ∈ Z.
⇒ tan 19pi/3 = tan 22pi/3 = tan 25pi/3, and so on.
Note: Since, tangent is an odd function, the value of tan(19pi/3) = tan(19pi/3).
Methods to Find Value of Tan 19pi/3
The tangent function is positive in the 1st quadrant. The value of tan 19pi/3 is given as 1.73205. . .. We can find the value of tan 19pi/3 by:
 Using Unit Circle
 Using Trigonometric Functions
Tan 19pi/3 Using Unit Circle
To find the value of tan 19pi/3 using the unit circle, represent 19pi/3 in the form (3 × 2pi) + pi/3 [∵ 19pi/3>2pi] ∵ The angle 19pi/3 is coterminal to pi/3 angle and also tangent is a periodic function, tan 19pi/3 = tan pi/3.
 Rotate ‘r’ anticlockwise to form pi/3 or 19pi/3 angle with the positive xaxis.
 The tan of 19pi/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 19pi/3 = y/x = 1.7321 (approx)
Tan 19pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 19pi/3 as:
 sin(19pi/3)/cos(19pi/3)
 ± sin(19pi/3)/√(1  sin²(19pi/3))
 ± √(1  cos²(19pi/3))/cos(19pi/3)
 ± 1/√(cosec²(19pi/3)  1)
 ± √(sec²(19pi/3)  1)
 1/cot(19pi/3)
Note: Since 19pi/3 lies in the 1st Quadrant, the final value of tan 19pi/3 will be positive.
We can use trigonometric identities to represent tan 19pi/3 as,
 cot(pi/2  19pi/3) = cot(35pi/6)
 cot(pi/2 + 19pi/3) = cot 41pi/6
 tan (pi  19pi/3) = tan(16pi/3)
☛ Also Check:
Examples Using Tan 19pi/3

Example 1: Simplify: 7 (tan(19pi/3)/cot(35pi/6))
Solution:
We know tan 19pi/3 = cot(35pi/6)
⇒ 7 tan(19pi/3)/cot(35pi/6) = 7 tan(19pi/3)/tan(19pi/3)
= 7(1) = 7 
Example 2: Find the value of (2 sin (19pi/6) cos (19pi/6) sec (19pi/3)). [Hint: Use tan 19pi/3 = 1.7321]
Solution:
Using sin 2a formula,
2 sin (19pi/6) cos (19pi/6) = sin (2 × 19pi/6) = sin 19pi/3
⇒ 2 sin (19pi/6) cos (19pi/6) sec(19pi/3) = sin(19pi/3) sec(19pi/3)
= sin(19pi/3)/cos(19pi/3) = tan 19pi/3
⇒ (2 sin (19pi/6) cos (19pi/6) sec(19pi/3)) = 1.7321 
Example 3: Using the value of tan 19pi/3, solve: (sec²(19pi/3)  1).
Solution:
We know, (sec²(19pi/3)  1) = (tan²(19pi/3)) = 3
⇒ (sec²(19pi/3)  1) = 3
FAQs on Tan 19pi/3
What is Tan 19pi/3?
Tan 19pi/3 is the value of tangent trigonometric function for an angle equal to 19π/3 radians. The value of tan 19pi/3 is √3 or 1.7321 (approx).
What is the Value of Tan 19pi/3 in Terms of Sin 19pi/3?
Using trigonometric identities, we can write tan 19pi/3 in terms of sin 19pi/3 as, tan(19pi/3) = sin(19pi/3)/√(1  sin²(19pi/3)) . Here, the value of sin 19pi/3 is equal to 0.866.
How to Find the Value of Tan 19pi/3?
The value of tan 19pi/3 can be calculated by constructing an angle of 19π/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 19pi/3 is equal to the ycoordinate(0.866) divided by the xcoordinate (0.5). ∴ tan 19pi/3 = √3 or 1.7321
How to Find Tan 19pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 19pi/3 can be given in terms of other trigonometric functions as:
 sin(19pi/3)/cos(19pi/3)
 ± sin(19pi/3)/√(1  sin²(19pi/3))
 ± √(1  cos²(19pi/3))/cos(19pi/3)
 ± 1/√(cosec²(19pi/3)  1)
 ± √(sec²(19pi/3)  1)
 1/cot(19pi/3)
☛ Also check: trigonometric table
What is the Exact Value of tan 19pi/3?
The exact value of tan 19pi/3 can be given accurately up to 8 decimal places as 1.73205080 or as √3.
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