Cosec 120

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/three) or sec (ii.0943951 . . .)

What is the Value of Sec 120 Degrees?

The value of sec 120 degrees is -2. Sec 120 degrees can as well be expressed using the equivalent of the given angle (120 degrees) in radians (ii.09439 . . .)

We know, using caste 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) = -two

Caption:

For sec 120 degrees, the bending 120° lies between ninety° and 180° (2d Quadrant). Since secant function is negative in the 2nd quadrant, thus sec 120° value = -two
Since the secant function is a periodic function, we can represent sec 120° as, sec 120 degrees = sec(120° + n × 360°), northward ∈ Z.
⇒ sec 120° = sec 480° = sec 840°, and and so on.
Annotation:
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 second quadrant. The value of sec 120° is given as -ii. We can notice the value of sec 120 degrees past:

• Using Unit Circumvolve
• Using Trigonometric Functions

Sec 120 Degrees Using Unit of measurement Circumvolve

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

• Rotate ‘r’ anticlockwise to form 120° angle with the positive ten-axis.
• The sec of 120 degrees equals the reciprocal of the x-coordinate(-0.5) of the bespeak of intersection (-0.five, 0.866) of unit circle and r.

Hence the value of sec 120° = 1/ten = -two

Sec 120° in Terms of Trigonometric Functions

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

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

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

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

• -sec(180° – 120°) = -sec sixty°
• -sec(180° + 120°) = -sec 300°
• cosec(90° + 120°) = cosec 210°
• cosec(90° – 120°) = cosec(-xxx°)

☛ Likewise Cheque:

• 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 part for an angle equal to 120 degrees.


The value of sec 120° is -ii.

How to Find the Value of Sec 120 Degrees?

The value of sec 120 degrees can be calculated past constructing an angle of 120° with the x-axis, and and so finding the coordinates of the corresponding point (-0.5, 0.866) on the unit circumvolve. The value of sec 120° is equal to the reciprocal of the 10-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° tin can be given in terms of other trigonometric functions as:

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

☛ Likewise check: trigonometric tabular array

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

Since the cosine function is the reciprocal of the secant function, we tin can write sec 120° as one/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 tin represent the secant function in terms of the cotangent function using trig identities, sec 120° tin exist written as √(1 + cot²(120°))/cot 120°. Here, the value of cot 120° is equal to -0.57735.