Sec 120 Degrees

The value of Sec 120 degrees is -2. Sec 120 degrees in radians is written as sec (120° × π/180°), i.e., sec (2π/3) or sec (2.094395. . .). In this article, we will discuss the methods to find the value of sec 120 degrees with examples.

• Sec 120°: -2
• Sec (-120 degrees): -2
• Sec 120° in radians: sec (2π/3) or sec (2.0943951 . . .)

What is the Value of Sec 120 Degrees?

The value of sec 120 degrees is -2. Sec 120 degrees can also be expressed using the equivalent of the given angle (120 degrees) in radians (2.09439 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 120 degrees = 120° × (π/180°) rad = 2π/3 or 2.0943 . . .
∴ sec 120° = sec(2.0943) = -2

Explanation:

For sec 120 degrees, the angle 120° lies between 90° and 180° (Second Quadrant). Since secant function is negative in the second quadrant, thus sec 120° value = -2
Since the secant function is a periodic function, we can represent sec 120° as, sec 120 degrees = sec(120° + n × 360°), n ∈ Z.
⇒ sec 120° = sec 480° = sec 840°, and so on.
Note: Since, secant is an even function, the value of sec(-120°) = sec(120°).

Methods to Find Value of Sec 120 Degrees

The secant function is negative in the 2nd quadrant. The value of sec 120° is given as -2. We can find the value of sec 120 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sec 120 Degrees Using Unit Circle

To find the value of sec 120 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 120° angle with the positive x-axis.
• The sec of 120 degrees equals the reciprocal of the x-coordinate(-0.5) of the point of intersection (-0.5, 0.866) of unit circle and r.

Hence the value of sec 120° = 1/x = -2

Sec 120° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 120 degrees as:

• ± 1/√(1 - sin²(120°))
• ± √(1 + tan²(120°))
• ± √(1 + cot²(120°))/cot 120°
• ± cosec 120°/√(cosec²(120°) - 1)
• 1/cos 120°

Note: Since 120° lies in the 2nd Quadrant, the final value of sec 120° will be negative.

We can use trigonometric identities to represent sec 120° as,

• -sec(180° - 120°) = -sec 60°
• -sec(180° + 120°) = -sec 300°
• cosec(90° + 120°) = cosec 210°
• cosec(90° - 120°) = cosec(-30°)

☛ Also Check:

• sec 510 degrees
• sec 270 degrees
• sec 420 degrees
• sec 135 degrees
• sec 60 degrees
• sec 28 degrees

FAQs on Sec 120 Degrees

What is Sec 120 Degrees?

Sec 120 degrees is the value of secant trigonometric function for an angle equal to 120 degrees. The value of sec 120° is -2.

How to Find the Value of Sec 120 Degrees?

The value of sec 120 degrees can be calculated by constructing an angle of 120° with the x-axis, and then finding the coordinates of the corresponding point (-0.5, 0.866) on the unit circle. The value of sec 120° is equal to the reciprocal of the x-coordinate(-0.5). ∴ sec 120° = -2.

How to Find Sec 120° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 120° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(120°))
• ± √(1 + tan²(120°))
• ± √(1 + cot²(120°))/cot 120°
• ± cosec 120°/√(cosec²(120°) - 1)
• 1/cos 120°

☛ Also check: trigonometric table

What is the Value of Sec 120° in Terms of Cos 120°?

Since the cosine function is the reciprocal of the secant function, we can write sec 120° as 1/cos(120°). The value of cos 120° is equal to -0.5.

What is the Value of Sec 120 Degrees in Terms of Cot 120°?

We can represent the secant function in terms of the cotangent function using trig identities, sec 120° can be written as √(1 + cot²(120°))/cot 120°. Here, the value of cot 120° is equal to -0.57735.