Tan 12 Degrees

The value of tan 12 degrees is 0.2125565. . .. Tan 12 degrees in radians is written as tan (12° × π/180°), i.e., tan (π/15) or tan (0.209439. . .). In this article, we will discuss the methods to find the value of tan 12 degrees with examples.

• Tan 12° in decimal: 0.2125565. . .
• Tan (-12 degrees): -0.2125565. . .
• Tan 12° in radians: tan (π/15) or tan (0.2094395 . . .)

What is the Value of Tan 12 Degrees?

The value of tan 12 degrees in decimal is 0.212556561. . .. Tan 12 degrees can also be expressed using the equivalent of the given angle (12 degrees) in radians (0.20943 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 12 degrees = 12° × (π/180°) rad = π/15 or 0.2094 . . .
∴ tan 12° = tan(0.2094) = 0.2125565. . .

Explanation:

For tan 12 degrees, the angle 12° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 12° value = 0.2125565. . .
Since the tangent function is a periodic function, we can represent tan 12° as, tan 12 degrees = tan(12° + n × 180°), n ∈ Z.
⇒ tan 12° = tan 192° = tan 372°, and so on.
Note: Since, tangent is an odd function, the value of tan(-12°) = -tan(12°).

Methods to Find Value of Tan 12 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 12° is given as 0.21255. . .. We can find the value of tan 12 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 12° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 12 degrees as:

• sin(12°)/cos(12°)
• ± sin 12°/√(1 - sin²(12°))
• ± √(1 - cos²(12°))/cos 12°
• ± 1/√(cosec²(12°) - 1)
• ± √(sec²(12°) - 1)
• 1/cot 12°

Note: Since 12° lies in the 1st Quadrant, the final value of tan 12° will be positive.

We can use trigonometric identities to represent tan 12° as,

• cot(90° - 12°) = cot 78°
• -cot(90° + 12°) = -cot 102°
• -tan (180° - 12°) = -tan 168°

Tan 12 Degrees Using Unit Circle

To find the value of tan 12 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 12° angle with the positive x-axis.
• The tan of 12 degrees equals the y-coordinate(0.2079) divided by x-coordinate(0.9781) of the point of intersection (0.9781, 0.2079) of unit circle and r.

Hence the value of tan 12° = y/x = 0.2126 (approx).

☛ Also Check:

• tan 60 degrees
• tan 135 degrees
• tan 225 degrees
• tan 68 degrees
• tan 420 degrees
• tan 69 degrees

FAQs on Tan 12 Degrees

What is Tan 12 Degrees?

Tan 12 degrees is the value of tangent trigonometric function for an angle equal to 12 degrees. The value of tan 12° is 0.2126 (approx).

How to Find Tan 12° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 12° can be given in terms of other trigonometric functions as:

• sin(12°)/cos(12°)
• ± sin 12°/√(1 - sin²(12°))
• ± √(1 - cos²(12°))/cos 12°
• ± 1/√(cosec²(12°) - 1)
• ± √(sec²(12°) - 1)
• 1/cot 12°

☛ Also check: trigonometric table

What is the Value of Tan 12° in Terms of Sec 12°?

We can represent the tangent function in terms of the secant function using trig identities, tan 12° can be written as √(sec²(12°) - 1). Here, the value of sec 12° is equal to 1.0223.

How to Find the Value of Tan 12 Degrees?

The value of tan 12 degrees can be calculated by constructing an angle of 12° with the x-axis, and then finding the coordinates of the corresponding point (0.9781, 0.2079) on the unit circle. The value of tan 12° is equal to the y-coordinate(0.2079) divided by the x-coordinate (0.9781). ∴ tan 12° = 0.2126

What is the Value of Tan 12 Degrees in Terms of Cot 12°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 12° as 1/cot(12°). The value of cot 12° is equal to 4.70463.