Tan 6 Degrees

The value of tan 6 degrees is 0.1051042. . .. Tan 6 degrees in radians is written as tan (6° × π/180°), i.e., tan (π/30) or tan (0.104719. . .). In this article, we will discuss the methods to find the value of tan 6 degrees with examples.

• Tan 6° in decimal: 0.1051042. . .
• Tan (-6 degrees): -0.1051042. . .
• Tan 6° in radians: tan (π/30) or tan (0.1047197 . . .)

What is the Value of Tan 6 Degrees?

The value of tan 6 degrees in decimal is 0.105104235. . .. Tan 6 degrees can also be expressed using the equivalent of the given angle (6 degrees) in radians (0.10471 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 6 degrees = 6° × (π/180°) rad = π/30 or 0.1047 . . .
∴ tan 6° = tan(0.1047) = 0.1051042. . .

Explanation:

For tan 6 degrees, the angle 6° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 6° value = 0.1051042. . .
Since the tangent function is a periodic function, we can represent tan 6° as, tan 6 degrees = tan(6° + n × 180°), n ∈ Z.
⇒ tan 6° = tan 186° = tan 366°, and so on.
Note: Since, tangent is an odd function, the value of tan(-6°) = -tan(6°).

Methods to Find Value of Tan 6 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 6° is given as 0.10510. . .. We can find the value of tan 6 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 6 Degrees Using Unit Circle

To find the value of tan 6 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 6° angle with the positive x-axis.
• The tan of 6 degrees equals the y-coordinate(0.1045) divided by x-coordinate(0.9945) of the point of intersection (0.9945, 0.1045) of unit circle and r.

Hence the value of tan 6° = y/x = 0.1051 (approx).

Tan 6° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 6 degrees as:

• sin(6°)/cos(6°)
• ± sin 6°/√(1 - sin²(6°))
• ± √(1 - cos²(6°))/cos 6°
• ± 1/√(cosec²(6°) - 1)
• ± √(sec²(6°) - 1)
• 1/cot 6°

Note: Since 6° lies in the 1st Quadrant, the final value of tan 6° will be positive.

We can use trigonometric identities to represent tan 6° as,

• cot(90° - 6°) = cot 84°
• -cot(90° + 6°) = -cot 96°
• -tan (180° - 6°) = -tan 174°

☛ Also Check:

• tan 30 degrees
• tan 0 degrees
• tan 270 degrees
• tan 67 degrees
• tan 130 degrees
• tan 73 degrees

FAQs on Tan 6 Degrees

What is Tan 6 Degrees?

Tan 6 degrees is the value of tangent trigonometric function for an angle equal to 6 degrees. The value of tan 6° is 0.1051 (approx).

How to Find Tan 6° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 6° can be given in terms of other trigonometric functions as:

• sin(6°)/cos(6°)
• ± sin 6°/√(1 - sin²(6°))
• ± √(1 - cos²(6°))/cos 6°
• ± 1/√(cosec²(6°) - 1)
• ± √(sec²(6°) - 1)
• 1/cot 6°

☛ Also check: trigonometric table

What is the Value of Tan 6° in Terms of Cosec 6°?

Since the tangent function can be represented using the cosecant function, we can write tan 6° as 1/√(cosec²(6°) - 1). The value of cosec 6° is equal to 9.56677.

How to Find the Value of Tan 6 Degrees?

The value of tan 6 degrees can be calculated by constructing an angle of 6° with the x-axis, and then finding the coordinates of the corresponding point (0.9945, 0.1045) on the unit circle. The value of tan 6° is equal to the y-coordinate(0.1045) divided by the x-coordinate (0.9945). ∴ tan 6° = 0.1051

What is the Value of Tan 6 Degrees in Terms of Cos 6°?

We know, using trig identities, we can write tan 6° as √(1 - cos²(6°))/cos 6°. Here, the value of cos 6° is equal to 0.994521.