Cos 8 Degrees

The value of cos 8 degrees is 0.9902680. . .. Cos 8 degrees in radians is written as cos (8° × π/180°), i.e., cos (2π/45) or cos (0.139626. . .). In this article, we will discuss the methods to find the value of cos 8 degrees with examples.

• Cos 8°: 0.9902680. . .
• Cos (-8 degrees): 0.9902680. . .
• Cos 8° in radians: cos (2π/45) or cos (0.1396263 . . .)

What is the Value of Cos 8 Degrees?

The value of cos 8 degrees in decimal is 0.990268068. . .. Cos 8 degrees can also be expressed using the equivalent of the given angle (8 degrees) in radians (0.13962 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 8 degrees = 8° × (π/180°) rad = 2π/45 or 0.1396 . . .
∴ cos 8° = cos(0.1396) = 0.9902680. . .

Explanation:

For cos 8 degrees, the angle 8° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 8° value = 0.9902680. . .
Since the cosine function is a periodic function, we can represent cos 8° as, cos 8 degrees = cos(8° + n × 360°), n ∈ Z.
⇒ cos 8° = cos 368° = cos 728°, and so on.
Note: Since, cosine is an even function, the value of cos(-8°) = cos(8°).

Methods to Find Value of Cos 8 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 8° is given as 0.99026. . .. We can find the value of cos 8 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 8 Degrees Using Unit Circle

To find the value of cos 8 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 8° angle with the positive x-axis.
• The cos of 8 degrees equals the x-coordinate(0.9903) of the point of intersection (0.9903, 0.1392) of unit circle and r.

Hence the value of cos 8° = x = 0.9903 (approx)

Cos 8° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 8 degrees as:

• ± √(1-sin²(8°))
• ± 1/√(1 + tan²(8°))
• ± cot 8°/√(1 + cot²(8°))
• ±√(cosec²(8°) - 1)/cosec 8°
• 1/sec 8°

Note: Since 8° lies in the 1st Quadrant, the final value of cos 8° will be positive.

We can use trigonometric identities to represent cos 8° as,

• -cos(180° - 8°) = -cos 172°
• -cos(180° + 8°) = -cos 188°
• sin(90° + 8°) = sin 98°
• sin(90° - 8°) = sin 82°

☛ Also Check:

• cos 240 degrees
• cos 1 degrees
• cos 135 degrees
• cos 780 degrees
• cos 840 degrees
• cos 405 degrees

FAQs on Cos 8 Degrees

What is Cos 8 Degrees?

Cos 8 degrees is the value of cosine trigonometric function for an angle equal to 8 degrees. The value of cos 8° is 0.9903 (approx)

What is the Value of Cos 8 Degrees in Terms of Sin 8°?

Using trigonometric identities, we can write cos 8° in terms of sin 8° as, cos(8°) = √(1 - sin²(8°)). Here, the value of sin 8° is equal to 0.1392.

How to Find Cos 8° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 8° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(8°))
• ± 1/√(1 + tan²(8°))
• ± cot 8°/√(1 + cot²(8°))
• ± √(cosec²(8°) - 1)/cosec 8°
• 1/sec 8°

☛ Also check: trigonometric table

What is the Value of Cos 8° in Terms of Cosec 8°?

Since the cosine function can be represented using the cosecant function, we can write cos 8° as [√(cosec²(8°) - 1)/cosec 8°]. The value of cosec 8° is equal to 7.18529.

How to Find the Value of Cos 8 Degrees?

The value of cos 8 degrees can be calculated by constructing an angle of 8° with the x-axis, and then finding the coordinates of the corresponding point (0.9903, 0.1392) on the unit circle. The value of cos 8° is equal to the x-coordinate (0.9903). ∴ cos 8° = 0.9903.