Sec 7pi/6
The value of sec 7pi/6 is 1.1547005. . .. Sec 7pi/6 radians in degrees is written as sec ((7π/6) × 180°/π), i.e., sec (210°). In this article, we will discuss the methods to find the value of sec 7pi/6 with examples.
 Sec 7pi/6: 2/√3
 Sec 7pi/6 in decimal: 1.1547005. . .
 Sec (7pi/6): 1.1547005. . . or 2/√3
 Sec 7pi/6 in degrees: sec (210°)
What is the Value of Sec 7pi/6?
The value of sec 7pi/6 in decimal is 1.154700538. . .. Sec 7pi/6 can also be expressed using the equivalent of the given angle (7pi/6) in degrees (210°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/6 radians = 7pi/6 × (180°/pi) = 210° or 210 degrees
∴ sec 7pi/6 = sec 7π/6 = sec(210°) = 2/√3 or 1.1547005. . .
Explanation:
For sec 7pi/6, the angle 7pi/6 lies between pi and 3pi/2 (Third Quadrant). Since secant function is negative in the third quadrant, thus sec 7pi/6 value = 2/√3 or 1.1547005. . .
Since the secant function is a periodic function, we can represent sec 7pi/6 as, sec 7pi/6 = sec(7pi/6 + n × 2pi), n ∈ Z.
⇒ sec 7pi/6 = sec 19pi/6 = sec 31pi/6 , and so on.
Note: Since, secant is an even function, the value of sec(7pi/6) = sec(7pi/6).
Methods to Find Value of Sec 7pi/6
The secant function is negative in the 3rd quadrant. The value of sec 7pi/6 is given as 1.15470. . .. We can find the value of sec 7pi/6 by:
 Using Unit Circle
 Using Trigonometric Functions
Sec 7pi/6 Using Unit Circle
To find the value of sec 7π/6 using the unit circle:
 Rotate ‘r’ anticlockwise to form 7pi/6 angle with the positive xaxis.
 The sec of 7pi/6 equals the reciprocal of the xcoordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.
Hence the value of sec 7pi/6 = 1/x = 1.1547 (approx)
Sec 7pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec 7pi/6 as:
 ± 1/√(1  sin²(7pi/6))
 ± √(1 + tan²(7pi/6))
 ± √(1 + cot²(7pi/6))/cot(7pi/6)
 ± cosec(7pi/6)/√(cosec²(7pi/6)  1)
 1/cos(7pi/6)
Note: Since 7pi/6 lies in the 3rd Quadrant, the final value of sec 7pi/6 will be negative.
We can use trigonometric identities to represent sec 7pi/6 as,
 sec(pi  7pi/6) = sec(pi/6)
 sec(pi + 7pi/6) = sec 13pi/6
 cosec(pi/2 + 7pi/6) = cosec 5pi/3
 cosec(pi/2  7pi/6) = cosec(2pi/3)
☛ Also Check:
Examples Using Sec 7pi/6

Example 1: Find the value of sec 7pi/6 if cos 7pi/6 is 0.8660.
Solution:
Since, sec 7pi/6 = 1/cos(7pi/6)
⇒ sec 7pi/6 = 1/(0.8660) = 1.1547 
Example 2: Using the value of sec 7pi/6, solve: (1 + tan²(7pi/6)).
Solution:
We know, (1 + tan²(7pi/6)) = (sec²(7pi/6)) = 1.3333
⇒ (1 + tan²(7pi/6)) = 1.3333 
Example 3: Simplify: 6 (sec(7pi/6)/cosec(5pi/3))
Solution:
We know sec 7pi/6 = cosec 5pi/3
⇒ 6 sec(7pi/6)/cosec(5pi/3) = 6 (sec(7pi/6)/sec(7pi/6))
= 6(1) = 6
FAQs on Sec 7pi/6
What is Sec 7pi/6?
Sec 7pi/6 is the value of secant trigonometric function for an angle equal to 7π/6. The value of sec 7pi/6 is 2/√3 or 1.1547 (approx).
How to Find Sec 7pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec 7pi/6 can be given in terms of other trigonometric functions as:
 ± 1/√(1  sin²(7pi/6))
 ± √(1 + tan²(7pi/6))
 ± √(1 + cot²(7pi/6))/cot(7pi/6)
 ± cosec(7pi/6)/√(cosec²(7pi/6)  1)
 1/cos(7pi/6)
☛ Also check: trigonometry table
What is the Value of Sec 7pi/6 in Terms of Cosec 7pi/6?
Since the secant function can be represented using the cosecant function, we can write sec 7pi/6 as [cosec(7pi/6)/√(cosec²(7pi/6)  1)]. The value of cosec 7pi/6 is equal to 2.
What is the Value of Sec 7pi/6 in Terms of Sin 7pi/6?
Using trigonometric identities, we can write sec 7pi/6 in terms of sin 7pi/6 as, sec(7pi/6) = 1/√(1  sin²(7pi/6)). Here, the value of sin 7pi/6 is equal to 0.5.
How to Find the Value of Sec 7pi/6?
The value of sec 7pi/6 can be calculated by constructing an angle of 7π/6 radians with the xaxis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of sec 7pi/6 is equal to the reciprocal of the xcoordinate(0.866). ∴ sec 7pi/6 = 1.1547.
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