Cos 85 Degrees

The value of cos 85 degrees is 0.0871557. . .. Cos 85 degrees in radians is written as cos (85° × π/180°), i.e., cos (17π/36) or cos (1.483529. . .). In this article, we will discuss the methods to find the value of cos 85 degrees with examples.

• Cos 85°: 0.0871557. . .
• Cos (-85 degrees): 0.0871557. . .
• Cos 85° in radians: cos (17π/36) or cos (1.4835298 . . .)

What is the Value of Cos 85 Degrees?

The value of cos 85 degrees in decimal is 0.087155742. . .. Cos 85 degrees can also be expressed using the equivalent of the given angle (85 degrees) in radians (1.48352 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 85 degrees = 85° × (π/180°) rad = 17π/36 or 1.4835 . . .
∴ cos 85° = cos(1.4835) = 0.0871557. . .

Explanation:

For cos 85 degrees, the angle 85° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 85° value = 0.0871557. . .
Since the cosine function is a periodic function, we can represent cos 85° as, cos 85 degrees = cos(85° + n × 360°), n ∈ Z.
⇒ cos 85° = cos 445° = cos 805°, and so on.
Note: Since, cosine is an even function, the value of cos(-85°) = cos(85°).

Methods to Find Value of Cos 85 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 85° is given as 0.08715. . .. We can find the value of cos 85 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 85° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 85 degrees as:

• ± √(1-sin²(85°))
• ± 1/√(1 + tan²(85°))
• ± cot 85°/√(1 + cot²(85°))
• ±√(cosec²(85°) - 1)/cosec 85°
• 1/sec 85°

Note: Since 85° lies in the 1st Quadrant, the final value of cos 85° will be positive.

We can use trigonometric identities to represent cos 85° as,

• -cos(180° - 85°) = -cos 95°
• -cos(180° + 85°) = -cos 265°
• sin(90° + 85°) = sin 175°
• sin(90° - 85°) = sin 5°

Cos 85 Degrees Using Unit Circle

To find the value of cos 85 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 85° angle with the positive x-axis.
• The cos of 85 degrees equals the x-coordinate(0.0872) of the point of intersection (0.0872, 0.9962) of unit circle and r.

Hence the value of cos 85° = x = 0.0872 (approx)

☛ Also Check:

• cos 53 degrees
• cos 135 degrees
• cos 15 degrees
• cos 61 degrees
• cos 320 degrees
• cos 47 degrees

FAQs on Cos 85 Degrees

What is Cos 85 Degrees?

Cos 85 degrees is the value of cosine trigonometric function for an angle equal to 85 degrees. The value of cos 85° is 0.0872 (approx)

How to Find the Value of Cos 85 Degrees?

The value of cos 85 degrees can be calculated by constructing an angle of 85° with the x-axis, and then finding the coordinates of the corresponding point (0.0872, 0.9962) on the unit circle. The value of cos 85° is equal to the x-coordinate (0.0872). ∴ cos 85° = 0.0872.

How to Find Cos 85° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 85° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(85°))
• ± 1/√(1 + tan²(85°))
• ± cot 85°/√(1 + cot²(85°))
• ± √(cosec²(85°) - 1)/cosec 85°
• 1/sec 85°

☛ Also check: trigonometry table

What is the Exact Value of cos 85 Degrees?

The exact value of cos 85 degrees can be given accurately up to 8 decimal places as 0.08715574.

What is the Value of Cos 85 Degrees in Terms of Cot 85°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 85° can be written as cot 85°/√(1 + cot²(85°)). Here, the value of cot 85° is equal to 0.08748.