Cos 280 Degrees

The value of cos 280 degrees is 0.1736481. . .. Cos 280 degrees in radians is written as cos (280° × π/180°), i.e., cos (14π/9) or cos (4.886921. . .). In this article, we will discuss the methods to find the value of cos 280 degrees with examples.

• Cos 280°: 0.1736481. . .
• Cos (-280 degrees): 0.1736481. . .
• Cos 280° in radians: cos (14π/9) or cos (4.8869219 . . .)

What is the Value of Cos 280 Degrees?

The value of cos 280 degrees in decimal is 0.173648177. . .. Cos 280 degrees can also be expressed using the equivalent of the given angle (280 degrees) in radians (4.88692 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 280 degrees = 280° × (π/180°) rad = 14π/9 or 4.8869 . . .
∴ cos 280° = cos(4.8869) = 0.1736481. . .

Explanation:

For cos 280 degrees, the angle 280° lies between 270° and 360° (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 280° value = 0.1736481. . .
Since the cosine function is a periodic function, we can represent cos 280° as, cos 280 degrees = cos(280° + n × 360°), n ∈ Z.
⇒ cos 280° = cos 640° = cos 1000°, and so on.
Note: Since, cosine is an even function, the value of cos(-280°) = cos(280°).

Methods to Find Value of Cos 280 Degrees

The cosine function is positive in the 4th quadrant. The value of cos 280° is given as 0.17364. . .. We can find the value of cos 280 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 280° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 280 degrees as:

• ± √(1-sin²(280°))
• ± 1/√(1 + tan²(280°))
• ± cot 280°/√(1 + cot²(280°))
• ±√(cosec²(280°) - 1)/cosec 280°
• 1/sec 280°

Note: Since 280° lies in the 4th Quadrant, the final value of cos 280° will be positive.

We can use trigonometric identities to represent cos 280° as,

• -cos(180° - 280°) = -cos(-100°)
• -cos(180° + 280°) = -cos 460°
• sin(90° + 280°) = sin 370°
• sin(90° - 280°) = sin(-190°)

Cos 280 Degrees Using Unit Circle

To find the value of cos 280 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 280° angle with the positive x-axis.
• The cos of 280 degrees equals the x-coordinate(0.1736) of the point of intersection (0.1736, -0.9848) of unit circle and r.

Hence the value of cos 280° = x = 0.1736 (approx)

☛ Also Check:

• cos 135 degrees
• cos 45 degrees
• cos 30 degrees
• cos 74 degrees
• cos 226 degrees
• cos 1110 degrees

FAQs on Cos 280 Degrees

What is Cos 280 Degrees?

Cos 280 degrees is the value of cosine trigonometric function for an angle equal to 280 degrees. The value of cos 280° is 0.1736 (approx)

What is the Value of Cos 280° in Terms of Cosec 280°?

Since the cosine function can be represented using the cosecant function, we can write cos 280° as -[√(cosec²(280°) - 1)/cosec 280°]. The value of cosec 280° is equal to -1.01542.

What is the Value of Cos 280 Degrees in Terms of Tan 280°?

We know, using trig identities, we can write cos 280° as 1/√(1 + tan²(280°)). Here, the value of tan 280° is equal to -5.671281.

How to Find Cos 280° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 280° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(280°))
• ± 1/√(1 + tan²(280°))
• ± cot 280°/√(1 + cot²(280°))
• ± √(cosec²(280°) - 1)/cosec 280°
• 1/sec 280°

☛ Also check: trigonometric table

How to Find the Value of Cos 280 Degrees?

The value of cos 280 degrees can be calculated by constructing an angle of 280° with the x-axis, and then finding the coordinates of the corresponding point (0.1736, -0.9848) on the unit circle. The value of cos 280° is equal to the x-coordinate (0.1736). ∴ cos 280° = 0.1736.