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.
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. . .
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 CircleTan 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
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.See more: Why Did Reggie Bush And Kim Break Up, Why Kim Kardashian & Reggie Bush Really Broke Up!
Hence the value of tan 60° = y/x = 1.7321 (approx).