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Tan 38 Degrees

The value of tan 38 degrees is 0.7812856. . .. Tan 38 degrees in radians is written as tan (38° × π/180°), i.e., tan (19π/90) or tan (0.663225. . .). In this article, we will discuss the methods to find the value of tan 38 degrees with examples.

Tan 38° in decimal: 0.7812856. . .
Tan (-38 degrees): -0.7812856. . .
Tan 38° in radians: tan (19π/90) or tan (0.6632251 . . .)

What is the Value of Tan 38 Degrees?

The value of tan 38 degrees in decimal is 0.781285626. . .. Tan 38 degrees can also be expressed using the equivalent of the given angle (38 degrees) in radians (0.66322 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 38 degrees = 38° × (π/180°) rad = 19π/90 or 0.6632 . . .
∴ tan 38° = tan(0.6632) = 0.7812856. . .

Explanation:

For tan 38 degrees, the angle 38° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 38° value = 0.7812856. . .
Since the tangent function is a periodic function, we can represent tan 38° as, tan 38 degrees = tan(38° + n × 180°), n ∈ Z.
⇒ tan 38° = tan 218° = tan 398°, and so on.
Note: Since, tangent is an odd function, the value of tan(-38°) = -tan(38°).

Methods to Find Value of Tan 38 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 38° is given as 0.78128. . .. We can find the value of tan 38 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 38 Degrees Using Unit Circle

To find the value of tan 38 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 38° angle with the positive x-axis.
The tan of 38 degrees equals the y-coordinate(0.6157) divided by x-coordinate(0.788) of the point of intersection (0.788, 0.6157) of unit circle and r.

Hence the value of tan 38° = y/x = 0.7813 (approx).

Tan 38° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 38 degrees as:

sin(38°)/cos(38°)
± sin 38°/√(1 - sin²(38°))
± √(1 - cos²(38°))/cos 38°
± 1/√(cosec²(38°) - 1)
± √(sec²(38°) - 1)
1/cot 38°

Note: Since 38° lies in the 1st Quadrant, the final value of tan 38° will be positive.

We can use trigonometric identities to represent tan 38° as,

cot(90° - 38°) = cot 52°
-cot(90° + 38°) = -cot 128°
-tan (180° - 38°) = -tan 142°

☛ Also Check:

Examples Using Tan 38 Degrees

Example 1: Simplify: 8 (tan 38°/cot 52°)

Solution:

We know tan 38° = cot 52°
⇒ 8 tan 38°/cot 52° = 8 (tan 38°/tan 38°)
= 8(1) = 8
Example 2: Find the value of (2 sin (19°) cos (19°) sec (38°)). [Hint: Use tan 38° = 0.7813]

Solution:

Using sin 2a formula,
2 sin (19°) cos (19°) = sin (2 × 19°) = sin 38°
⇒ 2 sin (19°) cos (19°) sec(38°) = sin 38° sec 38°
= sin 38°/cos 38° = tan 38°
⇒ (2 sin (19°) cos (19°) sec(38°)) = 0.7813
Example 3: Find the value of 2 tan(38°)/6 tan(142°).

Solution:

Using trigonometric identities, we know, tan(38°) = -tan(180° - 38°) = -tan 142°.
⇒ tan(38°) = -tan(142°)
⇒ Value of 2 tan(38°)/6 tan(142°) = -2/6 = -1/3

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FAQs on Tan 38 Degrees

What is Tan 38 Degrees?

Tan 38 degrees is the value of tangent trigonometric function for an angle equal to 38 degrees. The value of tan 38° is 0.7813 (approx).

How to Find Tan 38° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 38° can be given in terms of other trigonometric functions as:

sin(38°)/cos(38°)
± sin 38°/√(1 - sin²(38°))
± √(1 - cos²(38°))/cos 38°
± 1/√(cosec²(38°) - 1)
± √(sec²(38°) - 1)
1/cot 38°

☛ Also check: trigonometry table

What is the Value of Tan 38 Degrees in Terms of Cot 38°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 38° as 1/cot(38°). The value of cot 38° is equal to 1.27994.

What is the Exact Value of tan 38 Degrees?

The exact value of tan 38 degrees can be given accurately up to 8 decimal places as 0.78128562.

How to Find the Value of Tan 38 Degrees?

The value of tan 38 degrees can be calculated by constructing an angle of 38° with the x-axis, and then finding the coordinates of the corresponding point (0.788, 0.6157) on the unit circle. The value of tan 38° is equal to the y-coordinate(0.6157) divided by the x-coordinate (0.788). ∴ tan 38° = 0.7813

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