Tan 48 Degrees
The value of tan 48 degrees is 1.1106125. . .. Tan 48 degrees in radians is written as tan (48° × π/180°), i.e., tan (4π/15) or tan (0.837758. . .). In this article, we will discuss the methods to find the value of tan 48 degrees with examples.
- Tan 48° in decimal: 1.1106125. . .
- Tan (-48 degrees): -1.1106125. . .
- Tan 48° in radians: tan (4π/15) or tan (0.8377580 . . .)
What is the Value of Tan 48 Degrees?
The value of tan 48 degrees in decimal is 1.110612514. . .. Tan 48 degrees can also be expressed using the equivalent of the given angle (48 degrees) in radians (0.83775 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 48 degrees = 48° × (π/180°) rad = 4π/15 or 0.8377 . . .
∴ tan 48° = tan(0.8377) = 1.1106125. . .
Explanation:
For tan 48 degrees, the angle 48° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 48° value = 1.1106125. . .
Since the tangent function is a periodic function, we can represent tan 48° as, tan 48 degrees = tan(48° + n × 180°), n ∈ Z.
⇒ tan 48° = tan 228° = tan 408°, and so on.
Note: Since, tangent is an odd function, the value of tan(-48°) = -tan(48°).
Methods to Find Value of Tan 48 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 48° is given as 1.11061. . .. We can find the value of tan 48 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 48 Degrees Using Unit Circle
To find the value of tan 48 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 48° angle with the positive x-axis.
- The tan of 48 degrees equals the y-coordinate(0.7431) divided by x-coordinate(0.6691) of the point of intersection (0.6691, 0.7431) of unit circle and r.
Hence the value of tan 48° = y/x = 1.1106 (approx).
Tan 48° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 48 degrees as:
- sin(48°)/cos(48°)
- ± sin 48°/√(1 - sin²(48°))
- ± √(1 - cos²(48°))/cos 48°
- ± 1/√(cosec²(48°) - 1)
- ± √(sec²(48°) - 1)
- 1/cot 48°
Note: Since 48° lies in the 1st Quadrant, the final value of tan 48° will be positive.
We can use trigonometric identities to represent tan 48° as,
- cot(90° - 48°) = cot 42°
- -cot(90° + 48°) = -cot 138°
- -tan (180° - 48°) = -tan 132°
☛ Also Check:
FAQs on Tan 48 Degrees
What is Tan 48 Degrees?
Tan 48 degrees is the value of tangent trigonometric function for an angle equal to 48 degrees. The value of tan 48° is 1.1106 (approx).
What is the Value of Tan 48 Degrees in Terms of Cos 48°?
We know, using trig identities, we can write tan 48° as √(1 - cos²(48°))/cos 48°. Here, the value of cos 48° is equal to 0.669130.
What is the Value of Tan 48° in Terms of Sec 48°?
We can represent the tangent function in terms of the secant function using trig identities, tan 48° can be written as √(sec²(48°) - 1). Here, the value of sec 48° is equal to 1.4944.
How to Find the Value of Tan 48 Degrees?
The value of tan 48 degrees can be calculated by constructing an angle of 48° with the x-axis, and then finding the coordinates of the corresponding point (0.6691, 0.7431) on the unit circle. The value of tan 48° is equal to the y-coordinate(0.7431) divided by the x-coordinate (0.6691). ∴ tan 48° = 1.1106
How to Find Tan 48° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 48° can be given in terms of other trigonometric functions as:
- sin(48°)/cos(48°)
- ± sin 48°/√(1 - sin²(48°))
- ± √(1 - cos²(48°))/cos 48°
- ± 1/√(cosec²(48°) - 1)
- ± √(sec²(48°) - 1)
- 1/cot 48°
☛ Also check: trigonometry table