Tan 18 Degrees

The value of tan 18 degrees is 0.3249196. . .. Tan 18 degrees in radians is written as tan (18° × π/180°), i.e., tan (π/10) or tan (0.314159. . .). In this article, we will discuss the methods to find the value of tan 18 degrees with examples.

• Tan 18°: √(25 - 10√5)/5
• Tan 18° in decimal: 0.3249196. . .
• Tan (-18 degrees): -0.3249196. . . or -√(25 - 10√5)/5
• Tan 18° in radians: tan (π/10) or tan (0.3141592 . . .)

What is the Value of Tan 18 Degrees?

The value of tan 18 degrees in decimal is 0.324919696. . .. Tan 18 degrees can also be expressed using the equivalent of the given angle (18 degrees) in radians (0.31415 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 18 degrees = 18° × (π/180°) rad = π/10 or 0.3141 . . .
∴ tan 18° = tan(0.3141) = √(25 - 10√5)/5 or 0.3249196. . .

Explanation:

For tan 18 degrees, the angle 18° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 18° value = √(25 - 10√5)/5 or 0.3249196. . .
Since the tangent function is a periodic function, we can represent tan 18° as, tan 18 degrees = tan(18° + n × 180°), n ∈ Z.
⇒ tan 18° = tan 198° = tan 378°, and so on.
Note: Since, tangent is an odd function, the value of tan(-18°) = -tan(18°).

Methods to Find Value of Tan 18 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 18° is given as 0.32491. . .. We can find the value of tan 18 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 18° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 18 degrees as:

• sin(18°)/cos(18°)
• ± sin 18°/√(1 - sin²(18°))
• ± √(1 - cos²(18°))/cos 18°
• ± 1/√(cosec²(18°) - 1)
• ± √(sec²(18°) - 1)
• 1/cot 18°

Note: Since 18° lies in the 1st Quadrant, the final value of tan 18° will be positive.

We can use trigonometric identities to represent tan 18° as,

• cot(90° - 18°) = cot 72°
• -cot(90° + 18°) = -cot 108°
• -tan (180° - 18°) = -tan 162°

Tan 18 Degrees Using Unit Circle

To find the value of tan 18 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 18° angle with the positive x-axis.
• The tan of 18 degrees equals the y-coordinate(0.309) divided by x-coordinate(0.9511) of the point of intersection (0.9511, 0.309) of unit circle and r.

Hence the value of tan 18° = y/x = 0.3249 (approx).

☛ Also Check:

• tan 75 degrees
• tan 135 degrees
• tan 270 degrees
• tan 31 degrees
• tan 55 degrees
• tan 69 degrees

FAQs on Tan 18 Degrees

What is Tan 18 Degrees?

Tan 18 degrees is the value of tangent trigonometric function for an angle equal to 18 degrees. The value of tan 18° is √(25 - 10√5)/5 or 0.3249 (approx).

What is the Value of Tan 18° in Terms of Sec 18°?

We can represent the tangent function in terms of the secant function using trig identities, tan 18° can be written as √(sec²(18°) - 1). Here, the value of sec 18° is equal to 1.0514.

What is the Value of Tan 18 Degrees in Terms of Cos 18°?

We know, using trig identities, we can write tan 18° as √(1 - cos²(18°))/cos 18°. Here, the value of cos 18° is equal to 0.951056.

How to Find Tan 18° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 18° can be given in terms of other trigonometric functions as:

• sin(18°)/cos(18°)
• ± sin 18°/√(1 - sin²(18°))
• ± √(1 - cos²(18°))/cos 18°
• ± 1/√(cosec²(18°) - 1)
• ± √(sec²(18°) - 1)
• 1/cot 18°

☛ Also check: trigonometry table

How to Find the Value of Tan 18 Degrees?

The value of tan 18 degrees can be calculated by constructing an angle of 18° with the x-axis, and then finding the coordinates of the corresponding point (0.9511, 0.309) on the unit circle. The value of tan 18° is equal to the y-coordinate(0.309) divided by the x-coordinate (0.9511). ∴ tan 18° = √(25 - 10√5)/5 or 0.3249