Tan 11pi/6
The value of tan 11pi/6 is -0.5773502. . .. Tan 11pi/6 radians in degrees is written as tan ((11π/6) × 180°/π), i.e., tan (330°). In this article, we will discuss the methods to find the value of tan 11pi/6 with examples.
- Tan 11pi/6: -1/√3
- Tan 11pi/6 in decimal: -0.5773502. . .
- Tan (-11pi/6): 0.5773502. . . or 1/√3
- Tan 11pi/6 in degrees: tan (330°)
What is the Value of Tan 11pi/6?
The value of tan 11pi/6 in decimal is -0.577350269. . .. Tan 11pi/6 can also be expressed using the equivalent of the given angle (11pi/6) in degrees (330°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 11pi/6 radians = 11pi/6 × (180°/pi) = 330° or 330 degrees
∴ tan 11pi/6 = tan 11π/6 = tan(330°) = -1/√3 or -0.5773502. . .
Explanation:
For tan 11pi/6, the angle 11pi/6 lies between 3pi/2 and 2pi (Fourth Quadrant). Since tangent function is negative in the fourth quadrant, thus tan 11pi/6 value = -1/√3 or -0.5773502. . .
Since the tangent function is a periodic function, we can represent tan 11pi/6 as, tan 11pi/6 = tan(11pi/6 + n × pi), n ∈ Z.
⇒ tan 11pi/6 = tan 17pi/6 = tan 23pi/6 , and so on.
Note: Since, tangent is an odd function, the value of tan(-11pi/6) = -tan(11pi/6).
Methods to Find Value of Tan 11pi/6
The tangent function is negative in the 4th quadrant. The value of tan 11pi/6 is given as -0.57735. . .. We can find the value of tan 11pi/6 by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 11pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 11pi/6 as:
- sin(11pi/6)/cos(11pi/6)
- ± sin(11pi/6)/√(1 - sin²(11pi/6))
- ± √(1 - cos²(11pi/6))/cos(11pi/6)
- ± 1/√(cosec²(11pi/6) - 1)
- ± √(sec²(11pi/6) - 1)
- 1/cot(11pi/6)
Note: Since 11pi/6 lies in the 4th Quadrant, the final value of tan 11pi/6 will be negative.
We can use trigonometric identities to represent tan 11pi/6 as,
- cot(pi/2 - 11pi/6) = cot(-4pi/3)
- -cot(pi/2 + 11pi/6) = -cot 7pi/3
- -tan (pi - 11pi/6) = -tan(-5pi/6)
Tan 11pi/6 Using Unit Circle
To find the value of tan 11π/6 using the unit circle:
- Rotate ‘r’ anticlockwise to form 11pi/6 angle with the positive x-axis.
- The tan of 11pi/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 11pi/6 = y/x = -0.5774 (approx)
☛ Also Check:
FAQs on Tan 11pi/6
What is Tan 11pi/6?
Tan 11pi/6 is the value of tangent trigonometric function for an angle equal to 11π/6 radians. The value of tan 11pi/6 is -1/√3 or -0.5774 (approx).
What is the Value of Tan 11pi/6 in Terms of Sec 11pi/6?
We can represent the tangent function in terms of the secant function using trig identities, tan 11pi/6 can be written as -√(sec²(11pi/6) - 1). Here, the value of sec 11pi/6 is equal to 1.1547.
How to Find Tan 11pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 11pi/6 can be given in terms of other trigonometric functions as:
- sin(11pi/6)/cos(11pi/6)
- ± sin(11pi/6)/√(1 - sin²(11pi/6))
- ± √(1 - cos²(11pi/6))/cos(11pi/6)
- ± 1/√(cosec²(11pi/6) - 1)
- ± √(sec²(11pi/6) - 1)
- 1/cot(11pi/6)
☛ Also check: trigonometry table
How to Find the Value of Tan 11pi/6?
The value of tan 11pi/6 can be calculated by constructing an angle of 11π/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 11pi/6 is equal to the y-coordinate(-0.5) divided by the x-coordinate (0.866). ∴ tan 11pi/6 = -1/√3 or -0.5774
What is the Value of Tan 11pi/6 in Terms of Cot 11pi/6?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 11pi/6 as 1/cot(11pi/6). The value of cot 11pi/6 is equal to -√3.