# Cos 480

Cos 480

## Cos 480 Degrees

The value of
cos 480 degrees is -0.5. Cos 480 degrees in radians is written as cos (480° × π/180°), i.e., cos (8π/iii) or cos (8.377580. . .). In this commodity, we will talk over the methods to discover the value of cos 480 degrees with examples.

• Cos 480°:
-0.5
• Cos 480° in fraction:
-(1/2)
• Cos (-480 degrees):
-0.5

cos (8π/3) or cos (8.3775804 . . .)

## What is the Value of Cos 480 Degrees?

The value of cos 480 degrees in decimal is -0.5. Cos 480 degrees tin can also be expressed using the equivalent of the given angle (480 degrees) in radians (8.37758 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 480 degrees = 480° × (π/180°) rad = 8π/3 or 8.3775 . . .
∴ cos 480° = cos(viii.3775) = -(1/two) or -0.5

Caption:

For cos 480°, the angle 480° > 360°. Given the periodic property of the cosine office, we tin stand for it as cos(480° mod 360°) = cos(120°). The bending 480°, coterminal to angle 120°, is located in the Second Quadrant(Quadrant Two).
Since cosine office is negative in the 2d quadrant, thus cos 480 degrees value = -(one/two) or -0.five
Similarly, cos 480° can likewise be written as, cos 480 degrees = (480° + n × 360°), n ∈ Z.
⇒ cos 480° = cos 840° = cos 1200°, and and so on.
Note:
Since, cosine is an fifty-fifty office, the value of cos(-480°) = cos(480°).

## Methods to Notice Value of Cos 480 Degrees

The cosine part is negative in the 2nd quadrant. The value of cos 480° is given as -0.5. We can detect the value of cos 480 degrees past:

• Using Trigonometric Functions
• Using Unit of measurement Circle
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## Cos 480° in Terms of Trigonometric Functions

Using trigonometry formulas, we tin can represent the cos 480 degrees every bit:

• ± √(1-sin²(480°))
• ± 1/√(1 + tan²(480°))
• ± cot 480°/√(one + cot²(480°))
• ±√(cosec²(480°) – 1)/cosec 480°
• 1/sec 480°

Note: Since 480° lies in the 2nd Quadrant, the final value of cos 480° volition be negative.

We tin can employ trigonometric identities to represent cos 480° as,

• -cos(180° – 480°) = -cos(-300°)
• -cos(180° + 480°) = -cos 660°
• sin(90° + 480°) = sin 570°
• sin(90° – 480°) = sin(-390°)

## Cos 480 Degrees Using Unit Circumvolve

To find the value of cos 480 degrees using the unit of measurement circle, correspond 480° in the form (1 × 360°) + 120° [∵ 480°>360°] ∵ cosine is a periodic part, cos 480° = cos 120°.

• Rotate ‘r’ anticlockwise to form 120° or 480° angle with the positive x-centrality.
• The cos of 480 degrees equals the x-coordinate(-0.v) of the point of intersection (-0.5, 0.866) of unit of measurement circumvolve and r.

Hence the value of cos 480° = x = -0.5

☛ Likewise Bank check:

• cos 210 degrees
• cos 45 degrees
• cos 240 degrees
• cos 390 degrees
• cos 195 degrees
• cos 48 degrees

## FAQs on Cos 480 Degrees

### What is Cos 480 Degrees?

Cos 480 degrees is the value of cosine trigonometric role for an angle equal to 480 degrees.

The value of cos 480° is -(1/2) or -0.5

### What is the Value of Cos 480° in Terms of Cosec 480°?

Since the cosine part can be represented using the cosecant function, we can write cos 480° equally -[√(cosec²(480°) – 1)/cosec 480°]. The value of cosec 480° is equal to 1.15470.

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### What is the Value of Cos 480 Degrees in Terms of Tan 480°?

We know, using trig identities, nosotros tin can write cos 480° as -one/√(one + tan²(480°)). Here, the value of tan 480° is equal to -ane.732050.

### How to Observe Cos 480° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 480° can be given in terms of other trigonometric functions as:

• ± √(i-sin²(480°))
• ± i/√(1 + tan²(480°))
• ± cot 480°/√(i + cot²(480°))
• ± √(cosec²(480°) – 1)/cosec 480°
• ane/sec 480°

☛ Besides check: trigonometric table

### How to Find the Value of Cos 480 Degrees?

The value of cos 480 degrees can be calculated by constructing an angle of 480° with the x-axis, and so finding the coordinates of the corresponding betoken (-0.5, 0.866) on the unit circle. The value of cos 480° is equal to the x-coordinate (-0.v). ∴ cos 480° = -0.5.

### Cos 480

Source: https://www.cuemath.com/trigonometry/cos-480-degrees/