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Tan 16 Degrees

The value of tan 16 degrees is 0.2867453. . .. Tan 16 degrees in radians is written as tan (16° × π/180°), i.e., tan (4π/45) or tan (0.279252. . .). In this article, we will discuss the methods to find the value of tan 16 degrees with examples.

Tan 16° in decimal: 0.2867453. . .
Tan (-16 degrees): -0.2867453. . .
Tan 16° in radians: tan (4π/45) or tan (0.2792526 . . .)

What is the Value of Tan 16 Degrees?

The value of tan 16 degrees in decimal is 0.286745385. . .. Tan 16 degrees can also be expressed using the equivalent of the given angle (16 degrees) in radians (0.27925 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 16 degrees = 16° × (π/180°) rad = 4π/45 or 0.2792 . . .
∴ tan 16° = tan(0.2792) = 0.2867453. . .

Explanation:

For tan 16 degrees, the angle 16° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 16° value = 0.2867453. . .
Since the tangent function is a periodic function, we can represent tan 16° as, tan 16 degrees = tan(16° + n × 180°), n ∈ Z.
⇒ tan 16° = tan 196° = tan 376°, and so on.
Note: Since, tangent is an odd function, the value of tan(-16°) = -tan(16°).

Methods to Find Value of Tan 16 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 16° is given as 0.28674. . .. We can find the value of tan 16 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 16 Degrees Using Unit Circle

To find the value of tan 16 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 16° angle with the positive x-axis.
The tan of 16 degrees equals the y-coordinate(0.2756) divided by x-coordinate(0.9613) of the point of intersection (0.9613, 0.2756) of unit circle and r.

Hence the value of tan 16° = y/x = 0.2867 (approx).

Tan 16° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 16 degrees as:

sin(16°)/cos(16°)
± sin 16°/√(1 - sin²(16°))
± √(1 - cos²(16°))/cos 16°
± 1/√(cosec²(16°) - 1)
± √(sec²(16°) - 1)
1/cot 16°

Note: Since 16° lies in the 1st Quadrant, the final value of tan 16° will be positive.

We can use trigonometric identities to represent tan 16° as,

cot(90° - 16°) = cot 74°
-cot(90° + 16°) = -cot 106°
-tan (180° - 16°) = -tan 164°

☛ Also Check:

Examples Using Tan 16 Degrees

Example 1: Find the value of 9 tan(16°)/10 tan(164°).

Solution:

Using trigonometric identities, we know, tan(16°) = -tan(180° - 16°) = -tan 164°.
⇒ tan(16°) = -tan(164°)
⇒ Value of 9 tan(16°)/10 tan(164°) = -9/10
Example 2: Using the value of tan 16°, solve: (sec²(16°) - 1).

Solution:
We know, (sec²(16°) - 1) = (tan²(16°)) = 0.0822
⇒ (sec²(16°) - 1) = 0.0822
Example 3: Simplify: 3 (tan 16°/cot 74°)

Solution:

We know tan 16° = cot 74°
⇒ 3 tan 16°/cot 74° = 3 (tan 16°/tan 16°)
= 3(1) = 3

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FAQs on Tan 16 Degrees

What is Tan 16 Degrees?

Tan 16 degrees is the value of tangent trigonometric function for an angle equal to 16 degrees. The value of tan 16° is 0.2867 (approx).

What is the Value of Tan 16 Degrees in Terms of Cos 16°?

We know, using trig identities, we can write tan 16° as √(1 - cos²(16°))/cos 16°. Here, the value of cos 16° is equal to 0.961261.

What is the Value of Tan 16° in Terms of Sec 16°?

We can represent the tangent function in terms of the secant function using trig identities, tan 16° can be written as √(sec²(16°) - 1). Here, the value of sec 16° is equal to 1.0402.

How to Find the Value of Tan 16 Degrees?

The value of tan 16 degrees can be calculated by constructing an angle of 16° with the x-axis, and then finding the coordinates of the corresponding point (0.9613, 0.2756) on the unit circle. The value of tan 16° is equal to the y-coordinate(0.2756) divided by the x-coordinate (0.9613). ∴ tan 16° = 0.2867

How to Find Tan 16° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 16° can be given in terms of other trigonometric functions as:

sin(16°)/cos(16°)
± sin 16°/√(1 - sin²(16°))
± √(1 - cos²(16°))/cos 16°
± 1/√(cosec²(16°) - 1)
± √(sec²(16°) - 1)
1/cot 16°

☛ Also check: trigonometric table

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