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 480° in radians:
  
  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

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.

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.