Tan 2 Degrees

The value of tan 2 degrees is 0.0349207. . .. Tan 2 degrees in radians is written as tan (2° × π/180°), i.e., tan (π/90) or tan (0.034906. . .). In this article, we will discuss the methods to find the value of tan 2 degrees with examples.

• Tan 2° in decimal: 0.0349207. . .
• Tan (-2 degrees): -0.0349207. . .
• Tan 2° in radians: tan (π/90) or tan (0.0349065 . . .)

What is the Value of Tan 2 Degrees?

The value of tan 2 degrees in decimal is 0.034920769. . .. Tan 2 degrees can also be expressed using the equivalent of the given angle (2 degrees) in radians (0.03490 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 2 degrees = 2° × (π/180°) rad = π/90 or 0.0349 . . .
∴ tan 2° = tan(0.0349) = 0.0349207. . .

Explanation:

For tan 2 degrees, the angle 2° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 2° value = 0.0349207. . .
Since the tangent function is a periodic function, we can represent tan 2° as, tan 2 degrees = tan(2° + n × 180°), n ∈ Z.
⇒ tan 2° = tan 182° = tan 362°, and so on.
Note: Since, tangent is an odd function, the value of tan(-2°) = -tan(2°).

Methods to Find Value of Tan 2 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 2° is given as 0.03492. . .. We can find the value of tan 2 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 2° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 2 degrees as:

• sin(2°)/cos(2°)
• ± sin 2°/√(1 - sin²(2°))
• ± √(1 - cos²(2°))/cos 2°
• ± 1/√(cosec²(2°) - 1)
• ± √(sec²(2°) - 1)
• 1/cot 2°

Note: Since 2° lies in the 1st Quadrant, the final value of tan 2° will be positive.

We can use trigonometric identities to represent tan 2° as,

• cot(90° - 2°) = cot 88°
• -cot(90° + 2°) = -cot 92°
• -tan (180° - 2°) = -tan 178°

Tan 2 Degrees Using Unit Circle

To find the value of tan 2 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 2° angle with the positive x-axis.
• The tan of 2 degrees equals the y-coordinate(0.0349) divided by x-coordinate(0.9994) of the point of intersection (0.9994, 0.0349) of unit circle and r.

Hence the value of tan 2° = y/x = 0.0349 (approx).

☛ Also Check:

• tan 120 degrees
• tan 12 degrees
• tan 90 degrees
• tan 52 degrees
• tan 16 degrees
• tan 900 degrees

FAQs on Tan 2 Degrees

What is Tan 2 Degrees?

Tan 2 degrees is the value of tangent trigonometric function for an angle equal to 2 degrees. The value of tan 2° is 0.0349 (approx).

How to Find the Value of Tan 2 Degrees?

The value of tan 2 degrees can be calculated by constructing an angle of 2° with the x-axis, and then finding the coordinates of the corresponding point (0.9994, 0.0349) on the unit circle. The value of tan 2° is equal to the y-coordinate(0.0349) divided by the x-coordinate (0.9994). ∴ tan 2° = 0.0349

How to Find Tan 2° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 2° can be given in terms of other trigonometric functions as:

• sin(2°)/cos(2°)
• ± sin 2°/√(1 - sin²(2°))
• ± √(1 - cos²(2°))/cos 2°
• ± 1/√(cosec²(2°) - 1)
• ± √(sec²(2°) - 1)
• 1/cot 2°

☛ Also check: trigonometry table

What is the Value of Tan 2° in Terms of Sec 2°?

We can represent the tangent function in terms of the secant function using trig identities, tan 2° can be written as √(sec²(2°) - 1). Here, the value of sec 2° is equal to 1.0006.

What is the Value of Tan 2 Degrees in Terms of Cot 2°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 2° as 1/cot(2°). The value of cot 2° is equal to 28.63625.