Cos 260 Degrees

The value of cos 260 degrees is -0.1736481. . .. Cos 260 degrees in radians is written as cos (260° × π/180°), i.e., cos (13π/9) or cos (4.537856. . .). In this article, we will discuss the methods to find the value of cos 260 degrees with examples.

• Cos 260°: -0.1736481. . .
• Cos (-260 degrees): -0.1736481. . .
• Cos 260° in radians: cos (13π/9) or cos (4.5378560 . . .)

What is the Value of Cos 260 Degrees?

The value of cos 260 degrees in decimal is -0.173648177. . .. Cos 260 degrees can also be expressed using the equivalent of the given angle (260 degrees) in radians (4.53785 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 260 degrees = 260° × (π/180°) rad = 13π/9 or 4.5378 . . .
∴ cos 260° = cos(4.5378) = -0.1736481. . .

Explanation:

For cos 260 degrees, the angle 260° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 260° value = -0.1736481. . .
Since the cosine function is a periodic function, we can represent cos 260° as, cos 260 degrees = cos(260° + n × 360°), n ∈ Z.
⇒ cos 260° = cos 620° = cos 980°, and so on.
Note: Since, cosine is an even function, the value of cos(-260°) = cos(260°).

Methods to Find Value of Cos 260 Degrees

The cosine function is negative in the 3rd quadrant. The value of cos 260° is given as -0.17364. . .. We can find the value of cos 260 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 260 Degrees Using Unit Circle

To find the value of cos 260 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 260° angle with the positive x-axis.
• The cos of 260 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 260° = x = -0.1736 (approx)

Cos 260° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 260 degrees as:

• ± √(1-sin²(260°))
• ± 1/√(1 + tan²(260°))
• ± cot 260°/√(1 + cot²(260°))
• ±√(cosec²(260°) - 1)/cosec 260°
• 1/sec 260°

Note: Since 260° lies in the 3rd Quadrant, the final value of cos 260° will be negative.

We can use trigonometric identities to represent cos 260° as,

• -cos(180° - 260°) = -cos(-80°)
• -cos(180° + 260°) = -cos 440°
• sin(90° + 260°) = sin 350°
• sin(90° - 260°) = sin(-170°)

☛ Also Check:

• cos 210 degrees
• cos 360 degrees
• cos 60 degrees
• cos 16 degrees
• cos 67 degrees
• cos 630 degrees

FAQs on Cos 260 Degrees

What is Cos 260 Degrees?

Cos 260 degrees is the value of cosine trigonometric function for an angle equal to 260 degrees. The value of cos 260° is -0.1736 (approx)

What is the Value of Cos 260° in Terms of Cosec 260°?

Since the cosine function can be represented using the cosecant function, we can write cos 260° as [√(cosec²(260°) - 1)/cosec 260°]. The value of cosec 260° is equal to -1.01542.

How to Find Cos 260° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 260° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(260°))
• ± 1/√(1 + tan²(260°))
• ± cot 260°/√(1 + cot²(260°))
• ± √(cosec²(260°) - 1)/cosec 260°
• 1/sec 260°

☛ Also check: trigonometric table

How to Find the Value of Cos 260 Degrees?

The value of cos 260 degrees can be calculated by constructing an angle of 260° 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 260° is equal to the x-coordinate (-0.1736). ∴ cos 260° = -0.1736.

What is the Value of Cos 260 Degrees in Terms of Sin 260°?

Using trigonometric identities, we can write cos 260° in terms of sin 260° as, cos(260°) = -√(1 - sin²(260°)). Here, the value of sin 260° is equal to -0.9848.