Tan 25 Degrees
The value of tan 25 degrees is 0.4663076. . .. Tan 25 degrees in radians is written as tan (25° × π/180°), i.e., tan (5π/36) or tan (0.436332. . .). In this article, we will discuss the methods to find the value of tan 25 degrees with examples.
- Tan 25° in decimal: 0.4663076. . .
- Tan (-25 degrees): -0.4663076. . .
- Tan 25° in radians: tan (5π/36) or tan (0.4363323 . . .)
What is the Value of Tan 25 Degrees?
The value of tan 25 degrees in decimal is 0.466307658. . .. Tan 25 degrees can also be expressed using the equivalent of the given angle (25 degrees) in radians (0.43633 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 25 degrees = 25° × (π/180°) rad = 5π/36 or 0.4363 . . .
∴ tan 25° = tan(0.4363) = 0.4663076. . .
Explanation:
For tan 25 degrees, the angle 25° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 25° value = 0.4663076. . .
Since the tangent function is a periodic function, we can represent tan 25° as, tan 25 degrees = tan(25° + n × 180°), n ∈ Z.
⇒ tan 25° = tan 205° = tan 385°, and so on.
Note: Since, tangent is an odd function, the value of tan(-25°) = -tan(25°).
Methods to Find Value of Tan 25 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 25° is given as 0.46630. . .. We can find the value of tan 25 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 25° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 25 degrees as:
- sin(25°)/cos(25°)
- ± sin 25°/√(1 - sin²(25°))
- ± √(1 - cos²(25°))/cos 25°
- ± 1/√(cosec²(25°) - 1)
- ± √(sec²(25°) - 1)
- 1/cot 25°
Note: Since 25° lies in the 1st Quadrant, the final value of tan 25° will be positive.
We can use trigonometric identities to represent tan 25° as,
- cot(90° - 25°) = cot 65°
- -cot(90° + 25°) = -cot 115°
- -tan (180° - 25°) = -tan 155°
Tan 25 Degrees Using Unit Circle
To find the value of tan 25 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 25° angle with the positive x-axis.
- The tan of 25 degrees equals the y-coordinate(0.4226) divided by x-coordinate(0.9063) of the point of intersection (0.9063, 0.4226) of unit circle and r.
Hence the value of tan 25° = y/x = 0.4663 (approx).
☛ Also Check:
FAQs on Tan 25 Degrees
What is Tan 25 Degrees?
Tan 25 degrees is the value of tangent trigonometric function for an angle equal to 25 degrees. The value of tan 25° is 0.4663 (approx).
How to Find the Value of Tan 25 Degrees?
The value of tan 25 degrees can be calculated by constructing an angle of 25° with the x-axis, and then finding the coordinates of the corresponding point (0.9063, 0.4226) on the unit circle. The value of tan 25° is equal to the y-coordinate(0.4226) divided by the x-coordinate (0.9063). ∴ tan 25° = 0.4663
How to Find Tan 25° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 25° can be given in terms of other trigonometric functions as:
- sin(25°)/cos(25°)
- ± sin 25°/√(1 - sin²(25°))
- ± √(1 - cos²(25°))/cos 25°
- ± 1/√(cosec²(25°) - 1)
- ± √(sec²(25°) - 1)
- 1/cot 25°
☛ Also check: trigonometry table
What is the Exact Value of tan 25 Degrees?
The exact value of tan 25 degrees can be given accurately up to 8 decimal places as 0.46630765.
What is the Value of Tan 25 Degrees in Terms of Sin 25°?
Using trigonometric identities, we can write tan 25° in terms of sin 25° as, tan(25°) = sin 25°/√(1 - sin²(25°)) . Here, the value of sin 25° is equal to 0.4226.