Tan 15 Degrees
The value of tan 15 degrees is 0.2679491. . .. Tan 15 degrees in radians is written as tan (15° × π/180°), i.e., tan (π/12) or tan (0.261799. . .). In this article, we will discuss the methods to find the value of tan 15 degrees with examples.
- Tan 15°: 2 - √3
- Tan 15° in decimal: 0.2679491. . .
- Tan (-15 degrees): -0.2679491. . . or -2 + √3
- Tan 15° in radians: tan (π/12) or tan (0.2617993 . . .)
What is the Value of Tan 15 Degrees?
The value of tan 15 degrees in decimal is 0.267949192. . .. Tan 15 degrees can also be expressed using the equivalent of the given angle (15 degrees) in radians (0.26179 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 15 degrees = 15° × (π/180°) rad = π/12 or 0.2617 . . .
∴ tan 15° = tan(0.2617) = 2 - √3 or 0.2679491. . .
Explanation:
For tan 15 degrees, the angle 15° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 15° value = 2 - √3 or 0.2679491. . .
Since the tangent function is a periodic function, we can represent tan 15° as, tan 15 degrees = tan(15° + n × 180°), n ∈ Z.
⇒ tan 15° = tan 195° = tan 375°, and so on.
Note: Since, tangent is an odd function, the value of tan(-15°) = -tan(15°).
Methods to Find Value of Tan 15 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 15° is given as 0.26794. . .. We can find the value of tan 15 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 15 Degrees Using Unit Circle
To find the value of tan 15 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 15° angle with the positive x-axis.
- The tan of 15 degrees equals the y-coordinate(0.2588) divided by x-coordinate(0.9659) of the point of intersection (0.9659, 0.2588) of unit circle and r.
Hence the value of tan 15° = y/x = 0.2679 (approx).
Tan 15° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 15 degrees as:
- sin(15°)/cos(15°)
- ± sin 15°/√(1 - sin²(15°))
- ± √(1 - cos²(15°))/cos 15°
- ± 1/√(cosec²(15°) - 1)
- ± √(sec²(15°) - 1)
- 1/cot 15°
Note: Since 15° lies in the 1st Quadrant, the final value of tan 15° will be positive.
We can use trigonometric identities to represent tan 15° as,
- cot(90° - 15°) = cot 75°
- -cot(90° + 15°) = -cot 105°
- -tan (180° - 15°) = -tan 165°
☛ Also Check:
FAQs on Tan 15 Degrees
What is Tan 15 Degrees?
Tan 15 degrees is the value of tangent trigonometric function for an angle equal to 15 degrees. The value of tan 15° is 2 - √3 or 0.2679 (approx).
How to Find Tan 15° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 15° can be given in terms of other trigonometric functions as:
- sin(15°)/cos(15°)
- ± sin 15°/√(1 - sin²(15°))
- ± √(1 - cos²(15°))/cos 15°
- ± 1/√(cosec²(15°) - 1)
- ± √(sec²(15°) - 1)
- 1/cot 15°
☛ Also check: trigonometry table
How to Find the Value of Tan 15 Degrees?
The value of tan 15 degrees can be calculated by constructing an angle of 15° with the x-axis, and then finding the coordinates of the corresponding point (0.9659, 0.2588) on the unit circle. The value of tan 15° is equal to the y-coordinate(0.2588) divided by the x-coordinate (0.9659). ∴ tan 15° = 2 - √3 or 0.2679
What is the Value of Tan 15 Degrees in Terms of Sin 15°?
Using trigonometric identities, we can write tan 15° in terms of sin 15° as, tan(15°) = sin 15°/√(1 - sin²(15°)) . Here, the value of sin 15° is equal to (√6 - √2)/4.
What is the Value of Tan 15° in Terms of Cosec 15°?
Since the tangent function can be represented using the cosecant function, we can write tan 15° as 1/√(cosec²(15°) - 1). The value of cosec 15° is equal to 3.86370.