Tan 120 Degrees

The value of tan 120 degrees is -1.7320508. . .. Tan 120 degrees in radians is written as tan (120° × π/180°), i.e., tan (2π/3) or tan (2.094395. . .). In this article, we will discuss the methods to find the value of tan 120 degrees with examples.

• Tan 120°: -√3
• Tan 120° in decimal: -1.7320508. . .
• Tan (-120 degrees): 1.7320508. . . or √3
• Tan 120° in radians: tan (2π/3) or tan (2.0943951 . . .)

What is the Value of Tan 120 Degrees?

The value of tan 120 degrees in decimal is -1.732050807. . .. Tan 120 degrees can also be expressed using the equivalent of the given angle (120 degrees) in radians (2.09439 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 120 degrees = 120° × (π/180°) rad = 2π/3 or 2.0943 . . .
∴ tan 120° = tan(2.0943) = -√3 or -1.7320508. . .

Explanation:

For tan 120 degrees, the angle 120° lies between 90° and 180° (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 120° value = -√3 or -1.7320508. . .
Since the tangent function is a periodic function, we can represent tan 120° as, tan 120 degrees = tan(120° + n × 180°), n ∈ Z.
⇒ tan 120° = tan 300° = tan 480°, and so on.
Note: Since, tangent is an odd function, the value of tan(-120°) = -tan(120°).

Methods to Find Value of Tan 120 Degrees

The tangent function is negative in the 2nd quadrant. The value of tan 120° is given as -1.73205. . .. We can find the value of tan 120 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 120 Degrees Using Unit Circle

To find the value of tan 120 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 120° angle with the positive x-axis.
• The tan of 120 degrees equals the y-coordinate(0.866) divided by x-coordinate(-0.5) of the point of intersection (-0.5, 0.866) of unit circle and r.

Hence the value of tan 120° = y/x = -1.7321 (approx).

Tan 120° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 120 degrees as:

• sin(120°)/cos(120°)
• ± sin 120°/√(1 - sin²(120°))
• ± √(1 - cos²(120°))/cos 120°
• ± 1/√(cosec²(120°) - 1)
• ± √(sec²(120°) - 1)
• 1/cot 120°

Note: Since 120° lies in the 2nd Quadrant, the final value of tan 120° will be negative.

We can use trigonometric identities to represent tan 120° as,

• cot(90° - 120°) = cot(-30°)
• -cot(90° + 120°) = -cot 210°
• -tan (180° - 120°) = -tan 60°

☛ Also Check:

• tan 0 degrees
• tan 270 degrees
• tan 90 degrees
• tan 25 degrees
• tan 2000 degrees
• tan 1290 degrees

FAQs on Tan 120 Degrees

What is Tan 120 Degrees?

Tan 120 degrees is the value of tangent trigonometric function for an angle equal to 120 degrees. The value of tan 120° is -√3 or -1.7321 (approx).

How to Find the Value of Tan 120 Degrees?

The value of tan 120 degrees can be calculated by constructing an angle of 120° with the x-axis, and then finding the coordinates of the corresponding point (-0.5, 0.866) on the unit circle. The value of tan 120° is equal to the y-coordinate(0.866) divided by the x-coordinate (-0.5). ∴ tan 120° = -√3 or -1.7321

What is the Value of Tan 120 Degrees in Terms of Sin 120°?

Using trigonometric identities, we can write tan 120° in terms of sin 120° as, tan(120°) = -sin 120°/√(1 - sin²(120°)) . Here, the value of sin 120° is equal to √3/2.

How to Find Tan 120° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 120° can be given in terms of other trigonometric functions as:

• sin(120°)/cos(120°)
• ± sin 120°/√(1 - sin²(120°))
• ± √(1 - cos²(120°))/cos 120°
• ± 1/√(cosec²(120°) - 1)
• ± √(sec²(120°) - 1)
• 1/cot 120°

☛ Also check: trigonometry table

What is the Value of Tan 120° in Terms of Sec 120°?

We can represent the tangent function in terms of the secant function using trig identities, tan 120° can be written as -√(sec²(120°) - 1). Here, the value of sec 120° is equal to -2.