Tan pi/3

The value of tan pi/3 is 1.7320508. . .. Tan pi/3 radians in degrees is written as tan ((π/3) × 180°/π), i.e., tan (60°). In this article, we will discuss the methods to find the value of tan pi/3 with examples.

• Tan pi/3: √3
• Tan pi/3 in decimal: 1.7320508. . .
• Tan (-pi/3): -1.7320508. . . or -√3
• Tan pi/3 in degrees: tan (60°)

What is the Value of Tan pi/3?

The value of tan pi/3 in decimal is 1.732050807. . .. Tan pi/3 can also be expressed using the equivalent of the given angle (pi/3) in degrees (60°).

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

Explanation:

For tan pi/3, the angle pi/3 lies between 0 and pi/2 (First Quadrant). Since tangent function is positive in the first quadrant, thus tan pi/3 value = √3 or 1.7320508. . .
Since the tangent function is a periodic function, we can represent tan pi/3 as, tan pi/3 = tan(pi/3 + n × pi), n ∈ Z.
⇒ tan pi/3 = tan 4pi/3 = tan 7pi/3 , and so on.
Note: Since, tangent is an odd function, the value of tan(-pi/3) = -tan(pi/3).

Methods to Find Value of Tan pi/3

The tangent function is positive in the 1st quadrant. The value of tan pi/3 is given as 1.73205. . .. We can find the value of tan pi/3 by:

• Using Trigonometric Functions
• Using Unit Circle

Tan pi/3 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan pi/3 as:

• sin(pi/3)/cos(pi/3)
• ± sin(pi/3)/√(1 - sin²(pi/3))
• ± √(1 - cos²(pi/3))/cos(pi/3)
• ± 1/√(cosec²(pi/3) - 1)
• ± √(sec²(pi/3) - 1)
• 1/cot(pi/3)

Note: Since pi/3 lies in the 1st Quadrant, the final value of tan pi/3 will be positive.

We can use trigonometric identities to represent tan pi/3 as,

• cot(pi/2 - pi/3) = cot pi/6
• -cot(pi/2 + pi/3) = -cot 5pi/6
• -tan (pi - pi/3) = -tan 2pi/3

Tan pi/3 Using Unit Circle

To find the value of tan π/3 using the unit circle:

• Rotate ‘r’ anticlockwise to form pi/3 angle with the positive x-axis.
• The tan of pi/3 equals the y-coordinate(0.866) divided by the x-coordinate(0.5) of the point of intersection (0.5, 0.866) of unit circle and r.

Hence the value of tan pi/3 = y/x = 1.7321 (approx)

☛ Also Check:

• tan pi/4
• sec pi/2
• cos 11pi/6
• cos 2pi
• cos 3pi
• tan pi/12

FAQs on Tan pi/3

What is Tan pi/3?

Tan pi/3 is the value of tangent trigonometric function for an angle equal to π/3 radians. The value of tan pi/3 is √3 or 1.7321 (approx).

What is the Exact Value of tan pi/3?

The exact value of tan pi/3 can be given accurately up to 8 decimal places as 1.73205080 or as √3.

What is the Value of Tan pi/3 in Terms of Cos pi/3?

We know, using trig identities, we can write tan pi/3 as √(1 - cos²(pi/3))/cos pi/3. Here, the value of cos pi/3 is equal to 0.5.

How to Find the Value of Tan pi/3?

The value of tan pi/3 can be calculated by constructing an angle of π/3 radians 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 pi/3 is equal to the y-coordinate(0.866) divided by the x-coordinate (0.5). ∴ tan pi/3 = √3 or 1.7321

How to Find Tan pi/3 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan pi/3 can be given in terms of other trigonometric functions as:

• sin(pi/3)/cos(pi/3)
• ± sin(pi/3)/√(1 - sin²(pi/3))
• ± √(1 - cos²(pi/3))/cos(pi/3)
• ± 1/√(cosec²(pi/3) - 1)
• ± √(sec²(pi/3) - 1)
• 1/cot(pi/3)

☛ Also check: trigonometric table