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 x-axis.
• The tan of 8 degrees equals the y-coordinate(0.1392) divided by x-coordinate(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:

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• tan 10 degrees
• tan 20 degrees
• tan 140 degrees
• tan 210 degrees
• tan 480 degrees

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 x-axis, 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 y-coordinate(0.1392) divided by the x-coordinate (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