Tan 11 Degrees
The value of tan 11 degrees is 0.1943803. . .. Tan 11 degrees in radians is written as tan (11° × π/180°), i.e., tan (0.191986. . .). In this article, we will discuss the methods to find the value of tan 11 degrees with examples.
- Tan 11° in decimal: 0.1943803. . .
- Tan (-11 degrees): -0.1943803. . .
- Tan 11° in radians: tan (0.1919862 . . .)
What is the Value of Tan 11 Degrees?
The value of tan 11 degrees in decimal is 0.194380309. . .. Tan 11 degrees can also be expressed using the equivalent of the given angle (11 degrees) in radians (0.19198 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 11 degrees = 11° × (π/180°) rad = 0.1919 . . .
∴ tan 11° = tan(0.1919) = 0.1943803. . .
Explanation:
For tan 11 degrees, the angle 11° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 11° value = 0.1943803. . .
Since the tangent function is a periodic function, we can represent tan 11° as, tan 11 degrees = tan(11° + n × 180°), n ∈ Z.
⇒ tan 11° = tan 191° = tan 371°, and so on.
Note: Since, tangent is an odd function, the value of tan(-11°) = -tan(11°).
Methods to Find Value of Tan 11 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 11° is given as 0.19438. . .. We can find the value of tan 11 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 11 Degrees Using Unit Circle
To find the value of tan 11 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 11° angle with the positive x-axis.
- The tan of 11 degrees equals the y-coordinate(0.1908) divided by x-coordinate(0.9816) of the point of intersection (0.9816, 0.1908) of unit circle and r.
Hence the value of tan 11° = y/x = 0.1944 (approx).
Tan 11° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 11 degrees as:
- sin(11°)/cos(11°)
- ± sin 11°/√(1 - sin²(11°))
- ± √(1 - cos²(11°))/cos 11°
- ± 1/√(cosec²(11°) - 1)
- ± √(sec²(11°) - 1)
- 1/cot 11°
Note: Since 11° lies in the 1st Quadrant, the final value of tan 11° will be positive.
We can use trigonometric identities to represent tan 11° as,
- cot(90° - 11°) = cot 79°
- -cot(90° + 11°) = -cot 101°
- -tan (180° - 11°) = -tan 169°
☛ Also Check:
FAQs on Tan 11 Degrees
What is Tan 11 Degrees?
Tan 11 degrees is the value of tangent trigonometric function for an angle equal to 11 degrees. The value of tan 11° is 0.1944 (approx).
How to Find Tan 11° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 11° can be given in terms of other trigonometric functions as:
- sin(11°)/cos(11°)
- ± sin 11°/√(1 - sin²(11°))
- ± √(1 - cos²(11°))/cos 11°
- ± 1/√(cosec²(11°) - 1)
- ± √(sec²(11°) - 1)
- 1/cot 11°
☛ Also check: trigonometric table
How to Find the Value of Tan 11 Degrees?
The value of tan 11 degrees can be calculated by constructing an angle of 11° with the x-axis, and then finding the coordinates of the corresponding point (0.9816, 0.1908) on the unit circle. The value of tan 11° is equal to the y-coordinate(0.1908) divided by the x-coordinate (0.9816). ∴ tan 11° = 0.1944
What is the Value of Tan 11° in Terms of Sec 11°?
We can represent the tangent function in terms of the secant function using trig identities, tan 11° can be written as √(sec²(11°) - 1). Here, the value of sec 11° is equal to 1.0187.
What is the Value of Tan 11 Degrees in Terms of Cos 11°?
We know, using trig identities, we can write tan 11° as √(1 - cos²(11°))/cos 11°. Here, the value of cos 11° is equal to 0.981627.