Cos 285 Degrees

The value of cos 285 degrees is 0.2588190. . .. Cos 285 degrees in radians is written as cos (285° × π/180°), i.e., cos (19π/12) or cos (4.974188. . .). In this article, we will discuss the methods to find the value of cos 285 degrees with examples.

• Cos 285°: 0.2588190. . .
• Cos 285° in fraction: (√6-√2)/4
• Cos (-285 degrees): 0.2588190. . .
• Cos 285° in radians: cos (19π/12) or cos (4.9741883 . . .)

What is the Value of Cos 285 Degrees?

The value of cos 285 degrees in decimal is 0.258819045. . .. Cos 285 degrees can also be expressed using the equivalent of the given angle (285 degrees) in radians (4.97418 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 285 degrees = 285° × (π/180°) rad = 19π/12 or 4.9741 . . .
∴ cos 285° = cos(4.9741) = (√6-√2)/4 or 0.2588190. . .

Explanation:

For cos 285 degrees, the angle 285° lies between 270° and 360° (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 285° value = (√6-√2)/4 or 0.2588190. . .
Since the cosine function is a periodic function, we can represent cos 285° as, cos 285 degrees = cos(285° + n × 360°), n ∈ Z.
⇒ cos 285° = cos 645° = cos 1005°, and so on.
Note: Since, cosine is an even function, the value of cos(-285°) = cos(285°).

Methods to Find Value of Cos 285 Degrees

The cosine function is positive in the 4th quadrant. The value of cos 285° is given as 0.25881. . .. We can find the value of cos 285 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 285° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 285 degrees as:

• ± √(1-sin²(285°))
• ± 1/√(1 + tan²(285°))
• ± cot 285°/√(1 + cot²(285°))
• ±√(cosec²(285°) - 1)/cosec 285°
• 1/sec 285°

Note: Since 285° lies in the 4th Quadrant, the final value of cos 285° will be positive.

We can use trigonometric identities to represent cos 285° as,

• -cos(180° - 285°) = -cos(-105°)
• -cos(180° + 285°) = -cos 465°
• sin(90° + 285°) = sin 375°
• sin(90° - 285°) = sin(-195°)

Cos 285 Degrees Using Unit Circle

To find the value of cos 285 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 285° angle with the positive x-axis.
• The cos of 285 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 285° = x = 0.2588 (approx)

☛ Also Check:

• cos 21 degrees
• cos 40 degrees
• cos 0 degrees
• cos 585 degrees
• cos 115 degrees
• cos 23 degrees

FAQs on Cos 285 Degrees

What is Cos 285 Degrees?

Cos 285 degrees is the value of cosine trigonometric function for an angle equal to 285 degrees. The value of cos 285° is (√6-√2)/4 or 0.2588 (approx)

What is the Value of Cos 285 Degrees in Terms of Tan 285°?

We know, using trig identities, we can write cos 285° as 1/√(1 + tan²(285°)). Here, the value of tan 285° is equal to -3.732050.

What is the Exact Value of cos 285 Degrees?

The exact value of cos 285 degrees can be given accurately up to 8 decimal places as 0.25881904 and (√6-√2)/4 in fraction.

How to Find the Value of Cos 285 Degrees?

The value of cos 285 degrees can be calculated by constructing an angle of 285° 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 285° is equal to the x-coordinate (0.2588). ∴ cos 285° = 0.2588.

How to Find Cos 285° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 285° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(285°))
• ± 1/√(1 + tan²(285°))
• ± cot 285°/√(1 + cot²(285°))
• ± √(cosec²(285°) - 1)/cosec 285°
• 1/sec 285°

☛ Also check: trigonometry table