# Cosec 120

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 (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°).

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## 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.

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### 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.

## Cosec 120

Source: https://www.cuemath.com/trigonometry/sec-120-degrees/

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