Tan 30 Degrees

The value of tan 30 degrees is 0.5773502. . .. Tan 30 degrees in radians is written as tan (30° × π/180°), i.e., tan (π/6) or tan (0.523598. . .). In this article, we will discuss the methods to find the value of tan 30 degrees with examples.

• Tan 30°: 1/√3
• Tan 30° in decimal: 0.5773502. . .
• Tan (-30 degrees): -0.5773502. . . or -1/√3
• Tan 30° in radians: tan (π/6) or tan (0.5235987 . . .)

What is the Value of Tan 30 Degrees?

The value of tan 30 degrees in decimal is 0.577350269. . .. Tan 30 degrees can also be expressed using the equivalent of the given angle (30 degrees) in radians (0.52359 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 30 degrees = 30° × (π/180°) rad = π/6 or 0.5235 . . .
∴ tan 30° = tan(0.5235) = 1/√3 or 0.5773502. . .

Explanation:

For tan 30 degrees, the angle 30° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 30° value = 1/√3 or 0.5773502. . .
Since the tangent function is a periodic function, we can represent tan 30° as, tan 30 degrees = tan(30° + n × 180°), n ∈ Z.
⇒ tan 30° = tan 210° = tan 390°, and so on.
Note: Since, tangent is an odd function, the value of tan(-30°) = -tan(30°).

Methods to Find Value of Tan 30 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 30° is given as 0.57735. . .. We can find the value of tan 30 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 30° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 30 degrees as:

• sin(30°)/cos(30°)
• ± sin 30°/√(1 - sin²(30°))
• ± √(1 - cos²(30°))/cos 30°
• ± 1/√(cosec²(30°) - 1)
• ± √(sec²(30°) - 1)
• 1/cot 30°

Note: Since 30° lies in the 1st Quadrant, the final value of tan 30° will be positive.

We can use trigonometric identities to represent tan 30° as,

• cot(90° - 30°) = cot 60°
• -cot(90° + 30°) = -cot 120°
• -tan (180° - 30°) = -tan 150°

Tan 30 Degrees Using Unit Circle

To find the value of tan 30 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 30° angle with the positive x-axis.
• The tan of 30 degrees equals the y-coordinate(0.5) divided by x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence the value of tan 30° = y/x = 0.5774 (approx).

☛ Also Check:

• tan 45 degrees
• tan 270 degrees
• tan 135 degrees
• tan 23 degrees
• tan 54 degrees
• tan 16 degrees

FAQs on Tan 30 Degrees

What is Tan 30 Degrees?

Tan 30 degrees is the value of tangent trigonometric function for an angle equal to 30 degrees. The value of tan 30° is 1/√3 or 0.5774 (approx).

How to Find Tan 30° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 30° can be given in terms of other trigonometric functions as:

• sin(30°)/cos(30°)
• ± sin 30°/√(1 - sin²(30°))
• ± √(1 - cos²(30°))/cos 30°
• ± 1/√(cosec²(30°) - 1)
• ± √(sec²(30°) - 1)
• 1/cot 30°

☛ Also check: trigonometry table

How to Find the Value of Tan 30 Degrees?

The value of tan 30 degrees can be calculated by constructing an angle of 30° with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of tan 30° is equal to the y-coordinate(0.5) divided by the x-coordinate (0.866). ∴ tan 30° = 1/√3 or 0.5774

What is the Value of Tan 30° in Terms of Sec 30°?

We can represent the tangent function in terms of the secant function using trig identities, tan 30° can be written as √(sec²(30°) - 1). Here, the value of sec 30° is equal to 1.1547.

What is the Value of Tan 30 Degrees in Terms of Sin 30°?

Using trigonometric identities, we can write tan 30° in terms of sin 30° as, tan(30°) = sin 30°/√(1 - sin²(30°)) . Here, the value of sin 30° is equal to 1/2.