Tan 8 Degrees
The value of tan 8 degrees is 0.1405408. . .. Tan 8 degrees in radians is written as tan (8° × π/180°), i.e., tan (2π/45) or tan (0.139626. . .). In this article, we will discuss the methods to find the value of tan 8 degrees with examples.
 Tan 8° in decimal: 0.1405408. . .
 Tan (8 degrees): 0.1405408. . .
 Tan 8° in radians: tan (2π/45) or tan (0.1396263 . . .)
What is the Value of Tan 8 Degrees?
The value of tan 8 degrees in decimal is 0.140540834. . .. Tan 8 degrees can also be expressed using the equivalent of the given angle (8 degrees) in radians (0.13962 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 8 degrees = 8° × (π/180°) rad = 2π/45 or 0.1396 . . .
∴ tan 8° = tan(0.1396) = 0.1405408. . .
Explanation:
For tan 8 degrees, the angle 8° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 8° value = 0.1405408. . .
Since the tangent function is a periodic function, we can represent tan 8° as, tan 8 degrees = tan(8° + n × 180°), n ∈ Z.
⇒ tan 8° = tan 188° = tan 368°, and so on.
Note: Since, tangent is an odd function, the value of tan(8°) = tan(8°).
Methods to Find Value of Tan 8 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 8° is given as 0.14054. . .. We can find the value of tan 8 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Tan 8 Degrees Using Unit Circle
To find the value of tan 8 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 8° angle with the positive xaxis.
 The tan of 8 degrees equals the ycoordinate(0.1392) divided by xcoordinate(0.9903) of the point of intersection (0.9903, 0.1392) of unit circle and r.
Hence the value of tan 8° = y/x = 0.1405 (approx).
Tan 8° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 8 degrees as:
 sin(8°)/cos(8°)
 ± sin 8°/√(1  sin²(8°))
 ± √(1  cos²(8°))/cos 8°
 ± 1/√(cosec²(8°)  1)
 ± √(sec²(8°)  1)
 1/cot 8°
Note: Since 8° lies in the 1st Quadrant, the final value of tan 8° will be positive.
We can use trigonometric identities to represent tan 8° as,
 cot(90°  8°) = cot 82°
 cot(90° + 8°) = cot 98°
 tan (180°  8°) = tan 172°
☛ Also Check:
Examples Using Tan 8 Degrees

Example 1: Find the value of tan 8° if cot 8° is 7.1153.
Solution:
Since, tan 8° = 1/cot 8°
⇒ tan 8° = 1/7.1153 = 0.1405 
Example 2: Using the value of tan 8°, solve: (sec²(8°)  1).
Solution:
We know, (sec²(8°)  1) = (tan²(8°)) = 0.0198
⇒ (sec²(8°)  1) = 0.0198 
Example 3: Find the value of 2 tan 4°/(1  tan²(4°)). [Hint: Use tan 8° = 0.1405]
Solution:
Using the tan 2a formula,
2 tan 4°/(1  tan²(4°)) = tan(2 × 4°) = tan 8°
∵ tan 8° = 0.1405
⇒ 2 tan 4°/(1  tan²(4°)) = 0.1405
FAQs on Tan 8 Degrees
What is Tan 8 Degrees?
Tan 8 degrees is the value of tangent trigonometric function for an angle equal to 8 degrees. The value of tan 8° is 0.1405 (approx).
What is the Value of Tan 8° in Terms of Cosec 8°?
Since the tangent function can be represented using the cosecant function, we can write tan 8° as 1/√(cosec²(8°)  1). The value of cosec 8° is equal to 7.18529.
What is the Value of Tan 8 Degrees in Terms of Sin 8°?
Using trigonometric identities, we can write tan 8° in terms of sin 8° as, tan(8°) = sin 8°/√(1  sin²(8°)) . Here, the value of sin 8° is equal to 0.1392.
How to Find the Value of Tan 8 Degrees?
The value of tan 8 degrees can be calculated by constructing an angle of 8° with the xaxis, and then finding the coordinates of the corresponding point (0.9903, 0.1392) on the unit circle. The value of tan 8° is equal to the ycoordinate(0.1392) divided by the xcoordinate (0.9903). ∴ tan 8° = 0.1405
How to Find Tan 8° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 8° can be given in terms of other trigonometric functions as:
 sin(8°)/cos(8°)
 ± sin 8°/√(1  sin²(8°))
 ± √(1  cos²(8°))/cos 8°
 ± 1/√(cosec²(8°)  1)
 ± √(sec²(8°)  1)
 1/cot 8°
☛ Also check: trigonometry table
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