Tan 480 Degrees
The value of tan 480 degrees is -1.7320508. . .. Tan 480 degrees in radians is written as tan (480° × π/180°), i.e., tan (8π/3) or tan (8.377580. . .). In this article, we will discuss the methods to find the value of tan 480 degrees with examples.
- Tan 480°: -√3
- Tan 480° in decimal: -1.7320508. . .
- Tan (-480 degrees): 1.7320508. . . or √3
- Tan 480° in radians: tan (8π/3) or tan (8.3775804 . . .)
What is the Value of Tan 480 Degrees?
The value of tan 480 degrees in decimal is -1.732050807. . .. Tan 480 degrees can also be expressed using the equivalent of the given angle (480 degrees) in radians (8.37758 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 480 degrees = 480° × (π/180°) rad = 8π/3 or 8.3775 . . .
∴ tan 480° = tan(8.3775) = -√3 or -1.7320508. . .
Explanation:
For tan 480°, the angle 480° > 360°. We can represent tan 480° as, tan(480° mod 360°) = tan(120°). The angle 480°, coterminal to angle 120°, is located in the Second Quadrant(Quadrant II).
Since tangent function is negative in the 2nd quadrant, thus tan 480 degrees value = -√3 or -1.7320508. . .
Similarly, given the periodic property of tan 480°, it can also be written as, tan 480 degrees = (480° + n × 180°), n ∈ Z.
⇒ tan 480° = tan 660° = tan 840°, and so on.
Note: Since, tangent is an odd function, the value of tan(-480°) = -tan(480°).
Methods to Find Value of Tan 480 Degrees
The tangent function is negative in the 2nd quadrant. The value of tan 480° is given as -1.73205. . .. We can find the value of tan 480 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 480 Degrees Using Unit Circle
To find the value of tan 480 degrees using the unit circle, represent 480° in the form (1 × 360°) + 120° [∵ 480°>360°] ∵ The angle 480° is coterminal to 120° angle and also tangent is a periodic function, tan 480° = tan 120°.
- Rotate ‘r’ anticlockwise to form 120° or 480° angle with the positive x-axis.
- The tan of 480 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 480° = y/x = -1.7321 (approx).
Tan 480° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 480 degrees as:
- sin(480°)/cos(480°)
- ± sin 480°/√(1 - sin²(480°))
- ± √(1 - cos²(480°))/cos 480°
- ± 1/√(cosec²(480°) - 1)
- ± √(sec²(480°) - 1)
- 1/cot 480°
Note: Since 480° lies in the 2nd Quadrant, the final value of tan 480° will be negative.
We can use trigonometric identities to represent tan 480° as,
- cot(90° - 480°) = cot(-390°)
- -cot(90° + 480°) = -cot 570°
- -tan (180° - 480°) = -tan(-300°)
☛ Also Check:
FAQs on Tan 480 Degrees
What is Tan 480 Degrees?
Tan 480 degrees is the value of tangent trigonometric function for an angle equal to 480 degrees. The value of tan 480° is -√3 or -1.7321 (approx).
How to Find Tan 480° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 480° can be given in terms of other trigonometric functions as:
- sin(480°)/cos(480°)
- ± sin 480°/√(1 - sin²(480°))
- ± √(1 - cos²(480°))/cos 480°
- ± 1/√(cosec²(480°) - 1)
- ± √(sec²(480°) - 1)
- 1/cot 480°
☛ Also check: trigonometric table
How to Find the Value of Tan 480 Degrees?
The value of tan 480 degrees can be calculated by constructing an angle of 480° 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 480° is equal to the y-coordinate(0.866) divided by the x-coordinate (-0.5). ∴ tan 480° = -√3 or -1.7321
What is the Value of Tan 480 Degrees in Terms of Cos 480°?
We know, using trig identities, we can write tan 480° as √(1 - cos²(480°))/cos 480°. Here, the value of cos 480° is equal to -0.5.
What is the Exact Value of tan 480 Degrees?
The exact value of tan 480 degrees can be given accurately up to 8 decimal places as -1.73205080 or as -√3.