Tan 60 Degrees
The value of tan 60 degrees is 1.7320508. . .. Tan 60 degrees in radians is written as tan (60° × π/180°), i.e., tan (π/3) or tan (1.047197. . .). In this article, we will discuss the methods to find the value of tan 60 degrees with examples.
- Tan 60°: √3
- Tan 60° in decimal: 1.7320508. . .
- Tan (-60 degrees): -1.7320508. . . or -√3
- Tan 60° in radians: tan (π/3) or tan (1.0471975 . . .)
What is the Value of Tan 60 Degrees?
The value of tan 60 degrees in decimal is 1.732050807. . .. Tan 60 degrees can also be expressed using the equivalent of the given angle (60 degrees) in radians (1.04719 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 60 degrees = 60° × (π/180°) rad = π/3 or 1.0471 . . .
∴ tan 60° = tan(1.0471) = √3 or 1.7320508. . .
Explanation:
For tan 60 degrees, the angle 60° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 60° value = √3 or 1.7320508. . .
Since the tangent function is a periodic function, we can represent tan 60° as, tan 60 degrees = tan(60° + n × 180°), n ∈ Z.
⇒ tan 60° = tan 240° = tan 420°, and so on.
Note: Since, tangent is an odd function, the value of tan(-60°) = -tan(60°).
Methods to Find Value of Tan 60 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 60° is given as 1.73205. . .. We can find the value of tan 60 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 60° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 60 degrees as:
- sin(60°)/cos(60°)
- ± sin 60°/√(1 - sin²(60°))
- ± √(1 - cos²(60°))/cos 60°
- ± 1/√(cosec²(60°) - 1)
- ± √(sec²(60°) - 1)
- 1/cot 60°
Note: Since 60° lies in the 1st Quadrant, the final value of tan 60° will be positive.
We can use trigonometric identities to represent tan 60° as,
- cot(90° - 60°) = cot 30°
- -cot(90° + 60°) = -cot 150°
- -tan (180° - 60°) = -tan 120°
Tan 60 Degrees Using Unit Circle
To find the value of tan 60 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 60° angle with the positive x-axis.
- The tan of 60 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 60° = y/x = 1.7321 (approx).
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FAQs on Tan 60 Degrees
What is Tan 60 Degrees?
Tan 60 degrees is the value of tangent trigonometric function for an angle equal to 60 degrees. The value of tan 60° is √3 or 1.7321 (approx).
How to Find the Value of Tan 60 Degrees?
The value of tan 60 degrees can be calculated by constructing an angle of 60° 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 60° is equal to the y-coordinate(0.866) divided by the x-coordinate (0.5). ∴ tan 60° = √3 or 1.7321
What is the Value of Tan 60 Degrees in Terms of Cot 60°?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 60° as 1/cot(60°). The value of cot 60° is equal to 1/√3.
What is the Value of Tan 60° in Terms of Cosec 60°?
Since the tangent function can be represented using the cosecant function, we can write tan 60° as 1/√(cosec²(60°) - 1). The value of cosec 60° is equal to 1.15470.
How to Find Tan 60° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 60° can be given in terms of other trigonometric functions as:
- sin(60°)/cos(60°)
- ± sin 60°/√(1 - sin²(60°))
- ± √(1 - cos²(60°))/cos 60°
- ± 1/√(cosec²(60°) - 1)
- ± √(sec²(60°) - 1)
- 1/cot 60°
☛ Also check: trigonometry table