Tan 240 Degrees
The value of tan 240 degrees is 1.7320508. . .. Tan 240 degrees in radians is written as tan (240° × π/180°), i.e., tan (4π/3) or tan (4.188790. . .). In this article, we will discuss the methods to find the value of tan 240 degrees with examples.
- Tan 240°: √3
- Tan 240° in decimal: 1.7320508. . .
- Tan (-240 degrees): -1.7320508. . . or -√3
- Tan 240° in radians: tan (4π/3) or tan (4.1887902 . . .)
What is the Value of Tan 240 Degrees?
The value of tan 240 degrees in decimal is 1.732050807. . .. Tan 240 degrees can also be expressed using the equivalent of the given angle (240 degrees) in radians (4.18879 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 240 degrees = 240° × (π/180°) rad = 4π/3 or 4.1887 . . .
∴ tan 240° = tan(4.1887) = √3 or 1.7320508. . .
Explanation:
For tan 240 degrees, the angle 240° lies between 180° and 270° (Third Quadrant). Since tangent function is positive in the third quadrant, thus tan 240° value = √3 or 1.7320508. . .
Since the tangent function is a periodic function, we can represent tan 240° as, tan 240 degrees = tan(240° + n × 180°), n ∈ Z.
⇒ tan 240° = tan 420° = tan 600°, and so on.
Note: Since, tangent is an odd function, the value of tan(-240°) = -tan(240°).
Methods to Find Value of Tan 240 Degrees
The tangent function is positive in the 3rd quadrant. The value of tan 240° is given as 1.73205. . .. We can find the value of tan 240 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 240° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 240 degrees as:
- sin(240°)/cos(240°)
- ± sin 240°/√(1 - sin²(240°))
- ± √(1 - cos²(240°))/cos 240°
- ± 1/√(cosec²(240°) - 1)
- ± √(sec²(240°) - 1)
- 1/cot 240°
Note: Since 240° lies in the 3rd Quadrant, the final value of tan 240° will be positive.
We can use trigonometric identities to represent tan 240° as,
- cot(90° - 240°) = cot(-150°)
- -cot(90° + 240°) = -cot 330°
- -tan (180° - 240°) = -tan(-60°)
Tan 240 Degrees Using Unit Circle
To find the value of tan 240 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 240° angle with the positive x-axis.
- The tan of 240 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 240° = y/x = 1.7321 (approx).
☛ Also Check:
FAQs on Tan 240 Degrees
What is Tan 240 Degrees?
Tan 240 degrees is the value of tangent trigonometric function for an angle equal to 240 degrees. The value of tan 240° is √3 or 1.7321 (approx).
What is the Value of Tan 240 Degrees in Terms of Cos 240°?
We know, using trig identities, we can write tan 240° as -√(1 - cos²(240°))/cos 240°. Here, the value of cos 240° is equal to -0.5.
How to Find Tan 240° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 240° can be given in terms of other trigonometric functions as:
- sin(240°)/cos(240°)
- ± sin 240°/√(1 - sin²(240°))
- ± √(1 - cos²(240°))/cos 240°
- ± 1/√(cosec²(240°) - 1)
- ± √(sec²(240°) - 1)
- 1/cot 240°
☛ Also check: trigonometry table
How to Find the Value of Tan 240 Degrees?
The value of tan 240 degrees can be calculated by constructing an angle of 240° 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 240° is equal to the y-coordinate(-0.866) divided by the x-coordinate (-0.5). ∴ tan 240° = √3 or 1.7321
What is the Value of Tan 240° in Terms of Sec 240°?
We can represent the tangent function in terms of the secant function using trig identities, tan 240° can be written as √(sec²(240°) - 1). Here, the value of sec 240° is equal to -2.