Tan 13 Degrees

The value of tan 13 degrees is 0.2308681. . .. Tan 13 degrees in radians is written as tan (13° × π/180°), i.e., tan (0.226892. . .). In this article, we will discuss the methods to find the value of tan 13 degrees with examples.

• Tan 13° in decimal: 0.2308681. . .
• Tan (-13 degrees): -0.2308681. . .
• Tan 13° in radians: tan (0.2268928 . . .)

What is the Value of Tan 13 Degrees?

The value of tan 13 degrees in decimal is 0.230868191. . .. Tan 13 degrees can also be expressed using the equivalent of the given angle (13 degrees) in radians (0.22689 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 13 degrees = 13° × (π/180°) rad = 0.2268 . . .
∴ tan 13° = tan(0.2268) = 0.2308681. . .

Explanation:

For tan 13 degrees, the angle 13° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 13° value = 0.2308681. . .
Since the tangent function is a periodic function, we can represent tan 13° as, tan 13 degrees = tan(13° + n × 180°), n ∈ Z.
⇒ tan 13° = tan 193° = tan 373°, and so on.
Note: Since, tangent is an odd function, the value of tan(-13°) = -tan(13°).

Methods to Find Value of Tan 13 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 13° is given as 0.23086. . .. We can find the value of tan 13 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 13° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 13 degrees as:

• sin(13°)/cos(13°)
• ± sin 13°/√(1 - sin²(13°))
• ± √(1 - cos²(13°))/cos 13°
• ± 1/√(cosec²(13°) - 1)
• ± √(sec²(13°) - 1)
• 1/cot 13°

Note: Since 13° lies in the 1st Quadrant, the final value of tan 13° will be positive.

We can use trigonometric identities to represent tan 13° as,

• cot(90° - 13°) = cot 77°
• -cot(90° + 13°) = -cot 103°
• -tan (180° - 13°) = -tan 167°

Tan 13 Degrees Using Unit Circle

To find the value of tan 13 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 13° angle with the positive x-axis.
• The tan of 13 degrees equals the y-coordinate(0.225) divided by x-coordinate(0.9744) of the point of intersection (0.9744, 0.225) of unit circle and r.

Hence the value of tan 13° = y/x = 0.2309 (approx).

☛ Also Check:

• tan 40 degrees
• tan 360 degrees
• tan 75 degrees
• tan 4 degrees
• tan 55 degrees
• tan 100 degrees

FAQs on Tan 13 Degrees

What is Tan 13 Degrees?

Tan 13 degrees is the value of tangent trigonometric function for an angle equal to 13 degrees. The value of tan 13° is 0.2309 (approx).

How to Find the Value of Tan 13 Degrees?

The value of tan 13 degrees can be calculated by constructing an angle of 13° with the x-axis, and then finding the coordinates of the corresponding point (0.9744, 0.225) on the unit circle. The value of tan 13° is equal to the y-coordinate(0.225) divided by the x-coordinate (0.9744). ∴ tan 13° = 0.2309

What is the Value of Tan 13 Degrees in Terms of Cos 13°?

We know, using trig identities, we can write tan 13° as √(1 - cos²(13°))/cos 13°. Here, the value of cos 13° is equal to 0.974370.

What is the Value of Tan 13° in Terms of Cosec 13°?

Since the tangent function can be represented using the cosecant function, we can write tan 13° as 1/√(cosec²(13°) - 1). The value of cosec 13° is equal to 4.44541.

How to Find Tan 13° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 13° can be given in terms of other trigonometric functions as:

• sin(13°)/cos(13°)
• ± sin 13°/√(1 - sin²(13°))
• ± √(1 - cos²(13°))/cos 13°
• ± 1/√(cosec²(13°) - 1)
• ± √(sec²(13°) - 1)
• 1/cot 13°

☛ Also check: trigonometric table