The value of tan 12 degrees is 0.2125565. . .

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

What is the Value of tan 12 Degrees?

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

We know, using degree khổng lồ 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. . .

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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 tung 12° as, tung 12 degrees = tan(12° + n × 180°), n ∈ Z.⇒ rã 12° = chảy 192° = tan 372°, & so on.Note: Since, tangent is an odd function, the value of tan(-12°) = -tan(12°).

Methods khổng lồ Find Value of chảy 12 Degrees

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

Using Trigonometric FunctionsUsing Unit Circle

Tan 12° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the chảy 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 lớn 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

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To find the value of chảy 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 và r.

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

☛ Also Check:


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FAQs on chảy 12 Degrees

What is rã 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 lớn Find rã 12° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of chảy 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 rã 12° in Terms of Sec 12°?

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

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How to lớn Find the Value of tan 12 Degrees?

The value of chảy 12 degrees can be calculated by constructing an angle of 12° with the x-axis, và then finding the coordinates of the corresponding point (0.9781, 0.2079) on the unit circle. The value of chảy 12° is equal to the y-coordinate(0.2079) divided by the x-coordinate (0.9781). ∴ rã 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 chảy 12° as 1/cot(12°). The value of cot 12° is equal to lớn 4.70463.