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/3) or cos (8.377580. . .). In this article, we will discuss the methods to find 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 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(8.3775) = -(1/2) or -0.5
Explanation:
For cos 480°, the angle 480° > 360°. Given the periodic property of the cosine function, we can represent it as cos(480° mod 360°) = cos(120°). The angle 480°, coterminal to angle 120°, is located in the Second Quadrant(Quadrant II).
Since cosine function is negative in the 2nd quadrant, thus cos 480 degrees value = -(1/2) or -0.5
Similarly, cos 480° can also be written as, cos 480 degrees = (480° + n × 360°), n ∈ Z.
⇒ cos 480° = cos 840° = cos 1200°, and so on.
Note: Since, cosine is an even function, the value of cos(-480°) = cos(480°).
Methods to Find Value of Cos 480 Degrees
The cosine function is negative in the 2nd quadrant. The value of cos 480° is given as -0.5. We can find the value of cos 480 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 480° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 480 degrees as:
- ± √(1-sin²(480°))
- ± 1/√(1 + tan²(480°))
- ± cot 480°/√(1 + cot²(480°))
- ±√(cosec²(480°) - 1)/cosec 480°
- 1/sec 480°
Note: Since 480° lies in the 2nd Quadrant, the final value of cos 480° will be negative.
We can use 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 Circle
To find the value of cos 480 degrees using the unit circle, represent 480° in the form (1 × 360°) + 120° [∵ 480°>360°] ∵ cosine is a periodic function, cos 480° = cos 120°.
- Rotate ‘r’ anticlockwise to form 120° or 480° angle with the positive x-axis.
- The cos of 480 degrees equals the x-coordinate(-0.5) of the point of intersection (-0.5, 0.866) of unit circle and r.
Hence the value of cos 480° = x = -0.5
☛ Also Check:
FAQs on Cos 480 Degrees
What is Cos 480 Degrees?
Cos 480 degrees is the value of cosine trigonometric function 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 function can be represented using the cosecant function, we can write cos 480° as -[√(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, we can write cos 480° as -1/√(1 + tan²(480°)). Here, the value of tan 480° is equal to -1.732050.
How to Find 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:
- ± √(1-sin²(480°))
- ± 1/√(1 + tan²(480°))
- ± cot 480°/√(1 + cot²(480°))
- ± √(cosec²(480°) - 1)/cosec 480°
- 1/sec 480°
☛ Also 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 then finding the coordinates of the corresponding point (-0.5, 0.866) on the unit circle. The value of cos 480° is equal to the x-coordinate (-0.5). ∴ cos 480° = -0.5.