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Tan 19 Degrees

The value of tan 19 degrees is 0.3443276. . .. Tan 19 degrees in radians is written as tan (19° × π/180°), i.e., tan (0.331612. . .). In this article, we will discuss the methods to find the value of tan 19 degrees with examples.

Tan 19° in decimal: 0.3443276. . .
Tan (-19 degrees): -0.3443276. . .
Tan 19° in radians: tan (0.3316125 . . .)

What is the Value of Tan 19 Degrees?

The value of tan 19 degrees in decimal is 0.344327613. . .. Tan 19 degrees can also be expressed using the equivalent of the given angle (19 degrees) in radians (0.33161 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 19 degrees = 19° × (π/180°) rad = 0.3316 . . .
∴ tan 19° = tan(0.3316) = 0.3443276. . .

Explanation:

For tan 19 degrees, the angle 19° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 19° value = 0.3443276. . .
Since the tangent function is a periodic function, we can represent tan 19° as, tan 19 degrees = tan(19° + n × 180°), n ∈ Z.
⇒ tan 19° = tan 199° = tan 379°, and so on.
Note: Since, tangent is an odd function, the value of tan(-19°) = -tan(19°).

Methods to Find Value of Tan 19 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 19° is given as 0.34432. . .. We can find the value of tan 19 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 19° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 19 degrees as:

sin(19°)/cos(19°)
± sin 19°/√(1 - sin²(19°))
± √(1 - cos²(19°))/cos 19°
± 1/√(cosec²(19°) - 1)
± √(sec²(19°) - 1)
1/cot 19°

Note: Since 19° lies in the 1st Quadrant, the final value of tan 19° will be positive.

We can use trigonometric identities to represent tan 19° as,

cot(90° - 19°) = cot 71°
-cot(90° + 19°) = -cot 109°
-tan (180° - 19°) = -tan 161°

Tan 19 Degrees Using Unit Circle

To find the value of tan 19 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 19° angle with the positive x-axis.
The tan of 19 degrees equals the y-coordinate(0.3256) divided by x-coordinate(0.9455) of the point of intersection (0.9455, 0.3256) of unit circle and r.

Hence the value of tan 19° = y/x = 0.3443 (approx).

☛ Also Check:

Examples Using Tan 19 Degrees

Example 1: Simplify: 9 (tan 19°/cot 71°)

Solution:

We know tan 19° = cot 71°
⇒ 9 tan 19°/cot 71° = 9 (tan 19°/tan 19°)
= 9(1) = 9
Example 2: Find the value of (2 sin (9.5°) cos (9.5°) sec (19°)). [Hint: Use tan 19° = 0.3443]

Solution:

Using sin 2a formula,
2 sin (9.5°) cos (9.5°) = sin (2 × 9.5°) = sin 19°
⇒ 2 sin (9.5°) cos (9.5°) sec(19°) = sin 19° sec 19°
= sin 19°/cos 19° = tan 19°
⇒ (2 sin (9.5°) cos (9.5°) sec(19°)) = 0.3443
Example 3: Using the value of tan 19°, solve: (sec²(19°) - 1).

Solution:
We know, (sec²(19°) - 1) = (tan²(19°)) = 0.1186
⇒ (sec²(19°) - 1) = 0.1186

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FAQs on Tan 19 Degrees

What is Tan 19 Degrees?

Tan 19 degrees is the value of tangent trigonometric function for an angle equal to 19 degrees. The value of tan 19° is 0.3443 (approx).

How to Find Tan 19° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 19° can be given in terms of other trigonometric functions as:

sin(19°)/cos(19°)
± sin 19°/√(1 - sin²(19°))
± √(1 - cos²(19°))/cos 19°
± 1/√(cosec²(19°) - 1)
± √(sec²(19°) - 1)
1/cot 19°

☛ Also check: trigonometry table

How to Find the Value of Tan 19 Degrees?

The value of tan 19 degrees can be calculated by constructing an angle of 19° with the x-axis, and then finding the coordinates of the corresponding point (0.9455, 0.3256) on the unit circle. The value of tan 19° is equal to the y-coordinate(0.3256) divided by the x-coordinate (0.9455). ∴ tan 19° = 0.3443

What is the Value of Tan 19 Degrees in Terms of Sin 19°?

Using trigonometric identities, we can write tan 19° in terms of sin 19° as, tan(19°) = sin 19°/√(1 - sin²(19°)) . Here, the value of sin 19° is equal to 0.3256.

What is the Value of Tan 19° in Terms of Cosec 19°?

Since the tangent function can be represented using the cosecant function, we can write tan 19° as 1/√(cosec²(19°) - 1). The value of cosec 19° is equal to 3.07155.

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