A day full of math games & activities. Find one near you.

Sec 330 Degrees

The value of Sec 330 degrees is 1.1547005. . .. Sec 330 degrees in radians is written as sec (330° × π/180°), i.e., sec (11π/6) or sec (5.759586. . .). In this article, we will discuss the methods to find the value of sec 330 degrees with examples.

Sec 330°: 2/√3
Sec 330° in decimal: 1.1547005. . .
Sec (-330 degrees): 1.1547005. . . or 2/√3
Sec 330° in radians: sec (11π/6) or sec (5.7595865 . . .)

What is the Value of Sec 330 Degrees?

The value of sec 330 degrees in decimal is 1.154700538. . .. Sec 330 degrees can also be expressed using the equivalent of the given angle (330 degrees) in radians (5.75958 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 330 degrees = 330° × (π/180°) rad = 11π/6 or 5.7595 . . .
∴ sec 330° = sec(5.7595) = 2/√3 or 1.1547005. . .

Explanation:

For sec 330 degrees, the angle 330° lies between 270° and 360° (Fourth Quadrant). Since secant function is positive in the fourth quadrant, thus sec 330° value = 2/√3 or 1.1547005. . .
Since the secant function is a periodic function, we can represent sec 330° as, sec 330 degrees = sec(330° + n × 360°), n ∈ Z.
⇒ sec 330° = sec 690° = sec 1050°, and so on.
Note: Since, secant is an even function, the value of sec(-330°) = sec(330°).

Methods to Find Value of Sec 330 Degrees

The secant function is positive in the 4th quadrant. The value of sec 330° is given as 1.15470. . .. We can find the value of sec 330 degrees by:

Using Trigonometric Functions
Using Unit Circle

Sec 330° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 330 degrees as:

± 1/√(1 - sin²(330°))
± √(1 + tan²(330°))
± √(1 + cot²(330°))/cot 330°
± cosec 330°/√(cosec²(330°) - 1)
1/cos 330°

Note: Since 330° lies in the 4th Quadrant, the final value of sec 330° will be positive.

We can use trigonometric identities to represent sec 330° as,

-sec(180° - 330°) = -sec(-150°)
-sec(180° + 330°) = -sec 510°
cosec(90° + 330°) = cosec 420°
cosec(90° - 330°) = cosec(-240°)

Sec 330 Degrees Using Unit Circle

To find the value of sec 330 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 330° angle with the positive x-axis.
The sec of 330 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 330° = 1/x = 1.1547 (approx)

☛ Also Check:

Examples Using Sec 330 Degrees

Example 1: Simplify: 4 (sec 330°/cosec 420°)

Solution:

We know sec 330° = cosec 420°
⇒ 4 sec 330°/cosec 420° = 4 (sec 330°/sec 330°)
= 4(1) = 4
Example 2: Find the value of 1/(cos² 165° - sin² 165°). [Hint: Use sec 330° = 1.1547]

Solution:

Using the cos 2a formula,
1/(cos² 165° - sin² 165°) = 1/cos(2 × 165°) = sec 330°
∵ sec 330° = 1.1547
⇒ 1/(cos² 165° - sin² 165°) = 1.1547
Example 3: Using the value of sec 330°, solve: (1 + tan²(330°)).

Solution:
We know, (1 + tan²(330°)) = (sec²(330°)) = 1.3333
⇒ (1 + tan²(330°)) = 1.3333

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Sec 330 Degrees

What is Sec 330 Degrees?

Sec 330 degrees is the value of secant trigonometric function for an angle equal to 330 degrees. The value of sec 330° is 2/√3 or 1.1547 (approx).

What is the Value of Sec 330 Degrees in Terms of Sin 330°?

Using trigonometric identities, we can write sec 330° in terms of sin 330° as, sec(330°) = 1/√(1 - sin²(330°)). Here, the value of sin 330° is equal to -0.5.

How to Find Sec 330° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 330° can be given in terms of other trigonometric functions as:

± 1/√(1-sin²(330°))
± √(1 + tan²(330°))
± √(1 + cot²(330°))/cot 330°
± cosec 330°/√(cosec²(330°) - 1)
1/cos 330°

☛ Also check: trigonometry table

How to Find the Value of Sec 330 Degrees?

The value of sec 330 degrees can be calculated by constructing an angle of 330° 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 330° is equal to the reciprocal of the x-coordinate(0.866). ∴ sec 330° = 1.1547.

What is the Exact Value of Sec 330 Degrees?

The exact value of sec 330 degrees can be given accurately up to 8 decimal places as 1.15470053 or as 2/√3.

Download FREE Study Materials

Trigonometry

Math worksheets and
visual curriculum