Tan 210 Degrees

The value of tan 210 degrees is 0.5773502. . .. Tan 210 degrees in radians is written as tan (210° × π/180°), i.e., tan (7π/6) or tan (3.665191. . .). In this article, we will discuss the methods to find the value of tan 210 degrees with examples.

• Tan 210°: 1/√3
• Tan 210° in decimal: 0.5773502. . .
• Tan (-210 degrees): -0.5773502. . . or -1/√3
• Tan 210° in radians: tan (7π/6) or tan (3.6651914 . . .)

What is the Value of Tan 210 Degrees?

The value of tan 210 degrees in decimal is 0.577350269. . .. Tan 210 degrees can also be expressed using the equivalent of the given angle (210 degrees) in radians (3.66519 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 210 degrees = 210° × (π/180°) rad = 7π/6 or 3.6651 . . .
∴ tan 210° = tan(3.6651) = 1/√3 or 0.5773502. . .

Explanation:

For tan 210 degrees, the angle 210° lies between 180° and 270° (Third Quadrant). Since tangent function is positive in the third quadrant, thus tan 210° value = 1/√3 or 0.5773502. . .
Since the tangent function is a periodic function, we can represent tan 210° as, tan 210 degrees = tan(210° + n × 180°), n ∈ Z.
⇒ tan 210° = tan 390° = tan 570°, and so on.
Note: Since, tangent is an odd function, the value of tan(-210°) = -tan(210°).

Methods to Find Value of Tan 210 Degrees

The tangent function is positive in the 3rd quadrant. The value of tan 210° is given as 0.57735. . .. We can find the value of tan 210 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 210 Degrees Using Unit Circle

To find the value of tan 210 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 210° angle with the positive x-axis.
• The tan of 210 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 210° = y/x = 0.5774 (approx).

Tan 210° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 210 degrees as:

• sin(210°)/cos(210°)
• ± sin 210°/√(1 - sin²(210°))
• ± √(1 - cos²(210°))/cos 210°
• ± 1/√(cosec²(210°) - 1)
• ± √(sec²(210°) - 1)
• 1/cot 210°

Note: Since 210° lies in the 3rd Quadrant, the final value of tan 210° will be positive.

We can use trigonometric identities to represent tan 210° as,

• cot(90° - 210°) = cot(-120°)
• -cot(90° + 210°) = -cot 300°
• -tan (180° - 210°) = -tan(-30°)

☛ Also Check:

• tan 270 degrees
• tan 120 degrees
• tan 45 degrees
• tan 51 degrees
• tan 41 degrees
• tan 16 degrees

FAQs on Tan 210 Degrees

What is Tan 210 Degrees?

Tan 210 degrees is the value of tangent trigonometric function for an angle equal to 210 degrees. The value of tan 210° is 1/√3 or 0.5774 (approx).

How to Find Tan 210° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 210° can be given in terms of other trigonometric functions as:

• sin(210°)/cos(210°)
• ± sin 210°/√(1 - sin²(210°))
• ± √(1 - cos²(210°))/cos 210°
• ± 1/√(cosec²(210°) - 1)
• ± √(sec²(210°) - 1)
• 1/cot 210°

☛ Also check: trigonometric table

What is the Value of Tan 210° in Terms of Sec 210°?

We can represent the tangent function in terms of the secant function using trig identities, tan 210° can be written as √(sec²(210°) - 1). Here, the value of sec 210° is equal to -1.1547.

What is the Value of Tan 210 Degrees in Terms of Cos 210°?

We know, using trig identities, we can write tan 210° as -√(1 - cos²(210°))/cos 210°. Here, the value of cos 210° is equal to -0.866025.

How to Find the Value of Tan 210 Degrees?

The value of tan 210 degrees can be calculated by constructing an angle of 210° 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 210° is equal to the y-coordinate(-0.5) divided by the x-coordinate (-0.866). ∴ tan 210° = 1/√3 or 0.5774