Cos 255 Degrees
The value of cos 255 degrees is -0.2588190. . .. Cos 255 degrees in radians is written as cos (255° × π/180°), i.e., cos (17π/12) or cos (4.450589. . .). In this article, we will discuss the methods to find the value of cos 255 degrees with examples.
- Cos 255°: -0.2588190. . .
- Cos 255° in fraction: -(√6-√2)/4
- Cos (-255 degrees): -0.2588190. . .
- Cos 255° in radians: cos (17π/12) or cos (4.4505895 . . .)
What is the Value of Cos 255 Degrees?
The value of cos 255 degrees in decimal is -0.258819045. . .. Cos 255 degrees can also be expressed using the equivalent of the given angle (255 degrees) in radians (4.45058 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 255 degrees = 255° × (π/180°) rad = 17π/12 or 4.4505 . . .
∴ cos 255° = cos(4.4505) = -(√6-√2)/4 or -0.2588190. . .
Explanation:
For cos 255 degrees, the angle 255° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 255° value = -(√6-√2)/4 or -0.2588190. . .
Since the cosine function is a periodic function, we can represent cos 255° as, cos 255 degrees = cos(255° + n × 360°), n ∈ Z.
⇒ cos 255° = cos 615° = cos 975°, and so on.
Note: Since, cosine is an even function, the value of cos(-255°) = cos(255°).
Methods to Find Value of Cos 255 Degrees
The cosine function is negative in the 3rd quadrant. The value of cos 255° is given as -0.25881. . .. We can find the value of cos 255 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 255° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 255 degrees as:
- ± √(1-sin²(255°))
- ± 1/√(1 + tan²(255°))
- ± cot 255°/√(1 + cot²(255°))
- ±√(cosec²(255°) - 1)/cosec 255°
- 1/sec 255°
Note: Since 255° lies in the 3rd Quadrant, the final value of cos 255° will be negative.
We can use trigonometric identities to represent cos 255° as,
- -cos(180° - 255°) = -cos(-75°)
- -cos(180° + 255°) = -cos 435°
- sin(90° + 255°) = sin 345°
- sin(90° - 255°) = sin(-165°)
Cos 255 Degrees Using Unit Circle
To find the value of cos 255 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 255° angle with the positive x-axis.
- The cos of 255 degrees equals the x-coordinate(-0.2588) of the point of intersection (-0.2588, -0.9659) of unit circle and r.
Hence the value of cos 255° = x = -0.2588 (approx)
☛ Also Check:
FAQs on Cos 255 Degrees
What is Cos 255 Degrees?
Cos 255 degrees is the value of cosine trigonometric function for an angle equal to 255 degrees. The value of cos 255° is -(√6-√2)/4 or -0.2588 (approx)
How to Find Cos 255° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 255° can be given in terms of other trigonometric functions as:
- ± √(1-sin²(255°))
- ± 1/√(1 + tan²(255°))
- ± cot 255°/√(1 + cot²(255°))
- ± √(cosec²(255°) - 1)/cosec 255°
- 1/sec 255°
☛ Also check: trigonometric table
How to Find the Value of Cos 255 Degrees?
The value of cos 255 degrees can be calculated by constructing an angle of 255° with the x-axis, and then finding the coordinates of the corresponding point (-0.2588, -0.9659) on the unit circle. The value of cos 255° is equal to the x-coordinate (-0.2588). ∴ cos 255° = -0.2588.
What is the Value of Cos 255 Degrees in Terms of Tan 255°?
We know, using trig identities, we can write cos 255° as -1/√(1 + tan²(255°)). Here, the value of tan 255° is equal to 3.732050.
What is the Value of Cos 255° in Terms of Cosec 255°?
Since the cosine function can be represented using the cosecant function, we can write cos 255° as [√(cosec²(255°) - 1)/cosec 255°]. The value of cosec 255° is equal to -1.03527.