Sec 30 Degrees

The value of Sec 30 degrees is 1.1547005. . .. Sec 30 degrees in radians is written as sec (30° × π/180°), i.e., sec (π/6) or sec (0.523598. . .). In this article, we will discuss the methods to find the value of sec 30 degrees with examples.

• Sec 30°: 2/√3
• Sec 30° in decimal: 1.1547005. . .
• Sec (-30 degrees): 1.1547005. . . or 2/√3
• Sec 30° in radians: sec (π/6) or sec (0.5235987 . . .)

What is the Value of Sec 30 Degrees?

The value of sec 30 degrees in decimal is 1.154700538. . .. Sec 30 degrees can also be expressed using the equivalent of the given angle (30 degrees) in radians (0.52359 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 30 degrees = 30° × (π/180°) rad = π/6 or 0.5235 . . .
∴ sec 30° = sec(0.5235) = 2/√3 or 1.1547005. . .

Explanation:

For sec 30 degrees, the angle 30° lies between 0° and 90° (First Quadrant). Since secant function is positive in the first quadrant, thus sec 30° value = 2/√3 or 1.1547005. . .
Since the secant function is a periodic function, we can represent sec 30° as, sec 30 degrees = sec(30° + n × 360°), n ∈ Z.
⇒ sec 30° = sec 390° = sec 750°, and so on.
Note: Since, secant is an even function, the value of sec(-30°) = sec(30°).

Methods to Find Value of Sec 30 Degrees

The secant function is positive in the 1st quadrant. The value of sec 30° is given as 1.15470. . .. We can find the value of sec 30 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sec 30° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 30 degrees as:

• ± 1/√(1 - sin²(30°))
• ± √(1 + tan²(30°))
• ± √(1 + cot²(30°))/cot 30°
• ± cosec 30°/√(cosec²(30°) - 1)
• 1/cos 30°

Note: Since 30° lies in the 1st Quadrant, the final value of sec 30° will be positive.

We can use trigonometric identities to represent sec 30° as,

• -sec(180° - 30°) = -sec 150°
• -sec(180° + 30°) = -sec 210°
• cosec(90° + 30°) = cosec 120°
• cosec(90° - 30°) = cosec 60°

Sec 30 Degrees Using Unit Circle

To find the value of sec 30 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 30° angle with the positive x-axis.
• The sec of 30 degrees 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 30° = 1/x = 1.1547 (approx)

☛ Also Check:

• sec 150 degrees
• sec 330 degrees
• sec 47 degrees
• sec 90 degrees
• sec 60 degrees
• sec 270 degrees

FAQs on Sec 30 Degrees

What is Sec 30 Degrees?

Sec 30 degrees is the value of secant trigonometric function for an angle equal to 30 degrees. The value of sec 30° is 2/√3 or 1.1547 (approx).

What is the Value of Sec 30° in Terms of Cos 30°?

Since the cosine function is the reciprocal of the secant function, we can write sec 30° as 1/cos(30°). The value of cos 30° is equal to 0.866.

What is the Value of Sec 30 Degrees in Terms of Sin 30°?

Using trigonometric identities, we can write sec 30° in terms of sin 30° as, sec(30°) = 1/√(1 - sin²(30°)). Here, the value of sin 30° is equal to 0.5.

How to Find the Value of Sec 30 Degrees?

The value of sec 30 degrees can be calculated by constructing an angle of 30° 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 30° is equal to the reciprocal of the x-coordinate(0.866). ∴ sec 30° = 1.1547.

How to Find Sec 30° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 30° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(30°))
• ± √(1 + tan²(30°))
• ± √(1 + cot²(30°))/cot 30°
• ± cosec 30°/√(cosec²(30°) - 1)
• 1/cos 30°

☛ Also check: trigonometric table