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 x-axis.
• The sec of 7pi/6 equals the reciprocal of the x-coordinate(-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:

• sin 3pi
• sec 7pi/6
• cos 5pi/8
• cot pi
• sec pi
• tan 19pi/3

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 x-axis, 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 x-coordinate(-0.866). ∴ sec 7pi/6 = -1.1547.