Tan 7pi/3
The value of tan 7pi/3 is 1.7320508. . .. Tan 7pi/3 radians in degrees is written as tan ((7π/3) × 180°/π), i.e., tan (420°). In this article, we will discuss the methods to find the value of tan 7pi/3 with examples.
- Tan 7pi/3: √3
- Tan 7pi/3 in decimal: 1.7320508. . .
- Tan (-7pi/3): -1.7320508. . . or -√3
- Tan 7pi/3 in degrees: tan (420°)
What is the Value of Tan 7pi/3?
The value of tan 7pi/3 in decimal is 1.732050807. . .. Tan 7pi/3 can also be expressed using the equivalent of the given angle (7pi/3) in degrees (420°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/3 radians = 7pi/3 × (180°/pi) = 420° or 420 degrees
∴ tan 7pi/3 = tan 7π/3 = tan(420°) = √3 or 1.7320508. . .
Explanation:
For tan 7pi/3, the angle 7pi/3 > 2pi. We can represent tan 7pi/3 as, tan(7pi/3 mod 2pi) = tan(pi/3). The angle 7pi/3, coterminal to angle pi/3, is located in the First Quadrant(Quadrant I).
Since tan function is positive in the 1st quadrant, thus tan 7pi/3 value = √3 or 1.7320508. . .
Similarly, given the periodic property of tan 7pi/3, it can also be written as, tan 7pi/3 = (7pi/3 + n × pi), n ∈ Z.
⇒ tan 7pi/3 = tan 10pi/3 = tan 13pi/3, and so on.
Note: Since, tangent is an odd function, the value of tan(-7pi/3) = -tan(7pi/3).
Methods to Find Value of Tan 7pi/3
The tangent function is positive in the 1st quadrant. The value of tan 7pi/3 is given as 1.73205. . .. We can find the value of tan 7pi/3 by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 7pi/3 Using Unit Circle
To find the value of tan 7pi/3 using the unit circle, represent 7pi/3 in the form (1 × 2pi) + pi/3 [∵ 7pi/3>2pi] ∵ The angle 7pi/3 is coterminal to pi/3 angle and also tangent is a periodic function, tan 7pi/3 = tan pi/3.
- Rotate ‘r’ anticlockwise to form pi/3 or 7pi/3 angle with the positive x-axis.
- The tan of 7pi/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 7pi/3 = y/x = 1.7321 (approx)
Tan 7pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 7pi/3 as:
- sin(7pi/3)/cos(7pi/3)
- ± sin(7pi/3)/√(1 - sin²(7pi/3))
- ± √(1 - cos²(7pi/3))/cos(7pi/3)
- ± 1/√(cosec²(7pi/3) - 1)
- ± √(sec²(7pi/3) - 1)
- 1/cot(7pi/3)
Note: Since 7pi/3 lies in the 1st Quadrant, the final value of tan 7pi/3 will be positive.
We can use trigonometric identities to represent tan 7pi/3 as,
- cot(pi/2 - 7pi/3) = cot(-11pi/6)
- -cot(pi/2 + 7pi/3) = -cot 17pi/6
- -tan (pi - 7pi/3) = -tan(-4pi/3)
☛ Also Check:
FAQs on Tan 7pi/3
What is Tan 7pi/3?
Tan 7pi/3 is the value of tangent trigonometric function for an angle equal to 7π/3 radians. The value of tan 7pi/3 is √3 or 1.7321 (approx).
How to Find the Value of Tan 7pi/3?
The value of tan 7pi/3 can be calculated by constructing an angle of 7π/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 7pi/3 is equal to the y-coordinate(0.866) divided by the x-coordinate (0.5). ∴ tan 7pi/3 = √3 or 1.7321
How to Find Tan 7pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 7pi/3 can be given in terms of other trigonometric functions as:
- sin(7pi/3)/cos(7pi/3)
- ± sin(7pi/3)/√(1 - sin²(7pi/3))
- ± √(1 - cos²(7pi/3))/cos(7pi/3)
- ± 1/√(cosec²(7pi/3) - 1)
- ± √(sec²(7pi/3) - 1)
- 1/cot(7pi/3)
☛ Also check: trigonometric table
What is the Value of Tan 7pi/3 in Terms of Cot 7pi/3?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 7pi/3 as 1/cot(7pi/3). The value of cot 7pi/3 is equal to 1/√3.
What is the Value of Tan 7pi/3 in Terms of Cosec 7pi/3?
Since the tangent function can be represented using the cosecant function, we can write tan 7pi/3 as 1/√(cosec²(7pi/3) - 1). The value of cosec 7pi/3 is equal to 1.15470.