Tan 14 Degrees
The value of tan 14 degrees is 0.2493280. . .. Tan 14 degrees in radians is written as tan (14° × π/180°), i.e., tan (7π/90) or tan (0.244346. . .). In this article, we will discuss the methods to find the value of tan 14 degrees with examples.
- Tan 14° in decimal: 0.2493280. . .
- Tan (-14 degrees): -0.2493280. . .
- Tan 14° in radians: tan (7π/90) or tan (0.2443460 . . .)
What is the Value of Tan 14 Degrees?
The value of tan 14 degrees in decimal is 0.249328002. . .. Tan 14 degrees can also be expressed using the equivalent of the given angle (14 degrees) in radians (0.24434 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 14 degrees = 14° × (π/180°) rad = 7π/90 or 0.2443 . . .
∴ tan 14° = tan(0.2443) = 0.2493280. . .
Explanation:
For tan 14 degrees, the angle 14° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 14° value = 0.2493280. . .
Since the tangent function is a periodic function, we can represent tan 14° as, tan 14 degrees = tan(14° + n × 180°), n ∈ Z.
⇒ tan 14° = tan 194° = tan 374°, and so on.
Note: Since, tangent is an odd function, the value of tan(-14°) = -tan(14°).
Methods to Find Value of Tan 14 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 14° is given as 0.24932. . .. We can find the value of tan 14 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 14° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 14 degrees as:
- sin(14°)/cos(14°)
- ± sin 14°/√(1 - sin²(14°))
- ± √(1 - cos²(14°))/cos 14°
- ± 1/√(cosec²(14°) - 1)
- ± √(sec²(14°) - 1)
- 1/cot 14°
Note: Since 14° lies in the 1st Quadrant, the final value of tan 14° will be positive.
We can use trigonometric identities to represent tan 14° as,
- cot(90° - 14°) = cot 76°
- -cot(90° + 14°) = -cot 104°
- -tan (180° - 14°) = -tan 166°
Tan 14 Degrees Using Unit Circle
To find the value of tan 14 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 14° angle with the positive x-axis.
- The tan of 14 degrees equals the y-coordinate(0.2419) divided by x-coordinate(0.9703) of the point of intersection (0.9703, 0.2419) of unit circle and r.
Hence the value of tan 14° = y/x = 0.2493 (approx).
☛ Also Check:
FAQs on Tan 14 Degrees
What is Tan 14 Degrees?
Tan 14 degrees is the value of tangent trigonometric function for an angle equal to 14 degrees. The value of tan 14° is 0.2493 (approx).
What is the Exact Value of tan 14 Degrees?
The exact value of tan 14 degrees can be given accurately up to 8 decimal places as 0.24932800.
How to Find Tan 14° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 14° can be given in terms of other trigonometric functions as:
- sin(14°)/cos(14°)
- ± sin 14°/√(1 - sin²(14°))
- ± √(1 - cos²(14°))/cos 14°
- ± 1/√(cosec²(14°) - 1)
- ± √(sec²(14°) - 1)
- 1/cot 14°
☛ Also check: trigonometry table
What is the Value of Tan 14 Degrees in Terms of Cot 14°?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 14° as 1/cot(14°). The value of cot 14° is equal to 4.01078.
How to Find the Value of Tan 14 Degrees?
The value of tan 14 degrees can be calculated by constructing an angle of 14° with the x-axis, and then finding the coordinates of the corresponding point (0.9703, 0.2419) on the unit circle. The value of tan 14° is equal to the y-coordinate(0.2419) divided by the x-coordinate (0.9703). ∴ tan 14° = 0.2493