The value of tan 60 levels is 1.7320508. . .

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. Tan 60 degrees in radians is created as tan (60° × π/180°), i.e., tan (π/3) or tan (1.047197. . .). In this article, us will discuss the methods to discover the worth of tan 60 levels with examples.

Tan 60°: √3Tan 60° in decimal: 1.7320508. . .Tan (-60 degrees): -1.7320508. . . Or -√3Tan 60° in radians: tan (π/3) or tan (1.0471975 . . .)

What is the value of Tan 60 Degrees?

We know, using degree to radian conversion, θ in radians = θ in levels × (pi/180°)⇒ 60 degrees = 60° × (π/180°) rad = π/3 or 1.0471 . . .∴ tan 60° = tan(1.0471) = √3 or 1.7320508. . .

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Explanation:

For tan 60 degrees, the angle 60° lies in between 0° and also 90° (First Quadrant). Because tangent function is confident in the first quadrant, thus tan 60° worth = √3 or 1.7320508. . .Since the tangent function is a periodic function, we have the right to represent tan 60° as, tan 60 levels = tan(60° + n × 180°), n ∈ Z.⇒ tan 60° = tan 240° = tan 420°, and also so on.Note: Since, tangent is an odd function, the worth of tan(-60°) = -tan(60°).

Methods to discover Value the Tan 60 Degrees

The tangent function is optimistic in the 1st quadrant. The value of tan 60° is provided as 1.73205. . .. We can discover the worth of tan 60 degrees by:

Using Trigonometric FunctionsUsing Unit Circle

Tan 60° in terms of Trigonometric Functions

Using trigonometry formulas, we have the right to represent the tan 60 levels 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: due to the fact that 60° lies in the 1st Quadrant, the last value the tan 60° will certainly be positive.

We have the right to use trigonometric identities to stand for tan 60° as,

cot(90° - 60°) = cot 30°-cot(90° + 60°) = -cot 150°-tan (180° - 60°) = -tan 120°

Tan 60 levels Using Unit Circle

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To find the value of tan 60 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 60° angle with the confident x-axis.The tan of 60 levels equals the y-coordinate(0.866) separated by x-coordinate(0.5) the the point of intersection (0.5, 0.866) of unit circle and also r.

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Hence the value of tan 60° = y/x = 1.7321 (approx).