Tan 39 Degrees

The value of tan 39 degrees is 0.8097840. . .. Tan 39 degrees in radians is written as tan (39° × π/180°), i.e., tan (13π/60) or tan (0.680678. . .). In this article, we will discuss the methods to find the value of tan 39 degrees with examples.

• Tan 39° in decimal: 0.8097840. . .
• Tan (-39 degrees): -0.8097840. . .
• Tan 39° in radians: tan (13π/60) or tan (0.6806784 . . .)

What is the Value of Tan 39 Degrees?

The value of tan 39 degrees in decimal is 0.809784033. . .. Tan 39 degrees can also be expressed using the equivalent of the given angle (39 degrees) in radians (0.68067 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 39 degrees = 39° × (π/180°) rad = 13π/60 or 0.6806 . . .
∴ tan 39° = tan(0.6806) = 0.8097840. . .

Explanation:

For tan 39 degrees, the angle 39° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 39° value = 0.8097840. . .
Since the tangent function is a periodic function, we can represent tan 39° as, tan 39 degrees = tan(39° + n × 180°), n ∈ Z.
⇒ tan 39° = tan 219° = tan 399°, and so on.
Note: Since, tangent is an odd function, the value of tan(-39°) = -tan(39°).

Methods to Find Value of Tan 39 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 39° is given as 0.80978. . .. We can find the value of tan 39 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 39° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 39 degrees as:

• sin(39°)/cos(39°)
• ± sin 39°/√(1 - sin²(39°))
• ± √(1 - cos²(39°))/cos 39°
• ± 1/√(cosec²(39°) - 1)
• ± √(sec²(39°) - 1)
• 1/cot 39°

Note: Since 39° lies in the 1st Quadrant, the final value of tan 39° will be positive.

We can use trigonometric identities to represent tan 39° as,

• cot(90° - 39°) = cot 51°
• -cot(90° + 39°) = -cot 129°
• -tan (180° - 39°) = -tan 141°

Tan 39 Degrees Using Unit Circle

To find the value of tan 39 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 39° angle with the positive x-axis.
• The tan of 39 degrees equals the y-coordinate(0.6293) divided by x-coordinate(0.7771) of the point of intersection (0.7771, 0.6293) of unit circle and r.

Hence the value of tan 39° = y/x = 0.8098 (approx).

☛ Also Check:

• tan 10 degrees
• tan 12 degrees
• tan 135 degrees
• tan 7 degrees
• tan 5 degrees
• tan 49 degrees

FAQs on Tan 39 Degrees

What is Tan 39 Degrees?

Tan 39 degrees is the value of tangent trigonometric function for an angle equal to 39 degrees. The value of tan 39° is 0.8098 (approx).

How to Find the Value of Tan 39 Degrees?

The value of tan 39 degrees can be calculated by constructing an angle of 39° with the x-axis, and then finding the coordinates of the corresponding point (0.7771, 0.6293) on the unit circle. The value of tan 39° is equal to the y-coordinate(0.6293) divided by the x-coordinate (0.7771). ∴ tan 39° = 0.8098

How to Find Tan 39° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 39° can be given in terms of other trigonometric functions as:

• sin(39°)/cos(39°)
• ± sin 39°/√(1 - sin²(39°))
• ± √(1 - cos²(39°))/cos 39°
• ± 1/√(cosec²(39°) - 1)
• ± √(sec²(39°) - 1)
• 1/cot 39°

☛ Also check: trigonometry table

What is the Exact Value of tan 39 Degrees?

The exact value of tan 39 degrees can be given accurately up to 8 decimal places as 0.80978403.

What is the Value of Tan 39 Degrees in Terms of Cot 39°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 39° as 1/cot(39°). The value of cot 39° is equal to 1.23489.