Tan 24 Degrees
The value of tan 24 degrees is 0.4452286. . .. Tan 24 degrees in radians is written as tan (24° × π/180°), i.e., tan (2π/15) or tan (0.418879. . .). In this article, we will discuss the methods to find the value of tan 24 degrees with examples.
- Tan 24° in decimal: 0.4452286. . .
- Tan (-24 degrees): -0.4452286. . .
- Tan 24° in radians: tan (2π/15) or tan (0.4188790 . . .)
What is the Value of Tan 24 Degrees?
The value of tan 24 degrees in decimal is 0.445228685. . .. Tan 24 degrees can also be expressed using the equivalent of the given angle (24 degrees) in radians (0.41887 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 24 degrees = 24° × (π/180°) rad = 2π/15 or 0.4188 . . .
∴ tan 24° = tan(0.4188) = 0.4452286. . .
Explanation:
For tan 24 degrees, the angle 24° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 24° value = 0.4452286. . .
Since the tangent function is a periodic function, we can represent tan 24° as, tan 24 degrees = tan(24° + n × 180°), n ∈ Z.
⇒ tan 24° = tan 204° = tan 384°, and so on.
Note: Since, tangent is an odd function, the value of tan(-24°) = -tan(24°).
Methods to Find Value of Tan 24 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 24° is given as 0.44522. . .. We can find the value of tan 24 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 24 Degrees Using Unit Circle
To find the value of tan 24 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 24° angle with the positive x-axis.
- The tan of 24 degrees equals the y-coordinate(0.4067) divided by x-coordinate(0.9135) of the point of intersection (0.9135, 0.4067) of unit circle and r.
Hence the value of tan 24° = y/x = 0.4452 (approx).
Tan 24° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 24 degrees as:
- sin(24°)/cos(24°)
- ± sin 24°/√(1 - sin²(24°))
- ± √(1 - cos²(24°))/cos 24°
- ± 1/√(cosec²(24°) - 1)
- ± √(sec²(24°) - 1)
- 1/cot 24°
Note: Since 24° lies in the 1st Quadrant, the final value of tan 24° will be positive.
We can use trigonometric identities to represent tan 24° as,
- cot(90° - 24°) = cot 66°
- -cot(90° + 24°) = -cot 114°
- -tan (180° - 24°) = -tan 156°
☛ Also Check:
FAQs on Tan 24 Degrees
What is Tan 24 Degrees?
Tan 24 degrees is the value of tangent trigonometric function for an angle equal to 24 degrees. The value of tan 24° is 0.4452 (approx).
What is the Value of Tan 24 Degrees in Terms of Cot 24°?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 24° as 1/cot(24°). The value of cot 24° is equal to 2.24603.
What is the Value of Tan 24° in Terms of Sec 24°?
We can represent the tangent function in terms of the secant function using trig identities, tan 24° can be written as √(sec²(24°) - 1). Here, the value of sec 24° is equal to 1.0946.
How to Find Tan 24° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 24° can be given in terms of other trigonometric functions as:
- sin(24°)/cos(24°)
- ± sin 24°/√(1 - sin²(24°))
- ± √(1 - cos²(24°))/cos 24°
- ± 1/√(cosec²(24°) - 1)
- ± √(sec²(24°) - 1)
- 1/cot 24°
☛ Also check: trigonometry table
How to Find the Value of Tan 24 Degrees?
The value of tan 24 degrees can be calculated by constructing an angle of 24° with the x-axis, and then finding the coordinates of the corresponding point (0.9135, 0.4067) on the unit circle. The value of tan 24° is equal to the y-coordinate(0.4067) divided by the x-coordinate (0.9135). ∴ tan 24° = 0.4452