Cos 108 Degrees

The value of cos 108 degrees is -0.3090169. . .. Cos 108 degrees in radians is written as cos (108° × π/180°), i.e., cos (3π/5) or cos (1.884955. . .). In this article, we will discuss the methods to find the value of cos 108 degrees with examples.

• Cos 108°: -0.3090169. . .
• Cos 108° in fraction: (1 - √5)/4
• Cos (-108 degrees): -0.3090169. . .
• Cos 108° in radians: cos (3π/5) or cos (1.8849555 . . .)

What is the Value of Cos 108 Degrees?

The value of cos 108 degrees in decimal is -0.309016994. . .. Cos 108 degrees can also be expressed using the equivalent of the given angle (108 degrees) in radians (1.88495 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 108 degrees = 108° × (π/180°) rad = 3π/5 or 1.8849 . . .
∴ cos 108° = cos(1.8849) = (1 - √5)/4 or -0.3090169. . .

Explanation:

For cos 108 degrees, the angle 108° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 108° value = (1 - √5)/4 or -0.3090169. . .
Since the cosine function is a periodic function, we can represent cos 108° as, cos 108 degrees = cos(108° + n × 360°), n ∈ Z.
⇒ cos 108° = cos 468° = cos 828°, and so on.
Note: Since, cosine is an even function, the value of cos(-108°) = cos(108°).

Methods to Find Value of Cos 108 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 108° is given as -0.30901. . .. We can find the value of cos 108 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 108 Degrees Using Unit Circle

To find the value of cos 108 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 108° angle with the positive x-axis.
• The cos of 108 degrees equals the x-coordinate(-0.309) of the point of intersection (-0.309, 0.9511) of unit circle and r.

Hence the value of cos 108° = x = -0.309 (approx)

Cos 108° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 108 degrees as:

• ± √(1-sin²(108°))
• ± 1/√(1 + tan²(108°))
• ± cot 108°/√(1 + cot²(108°))
• ±√(cosec²(108°) - 1)/cosec 108°
• 1/sec 108°

Note: Since 108° lies in the 2nd Quadrant, the final value of cos 108° will be negative.

We can use trigonometric identities to represent cos 108° as,

• -cos(180° - 108°) = -cos 72°
• -cos(180° + 108°) = -cos 288°
• sin(90° + 108°) = sin 198°
• sin(90° - 108°) = sin(-18°)

☛ Also Check:

• cos 120 degrees
• cos 150 degrees
• cos 90 degrees
• cos 24 degrees
• cos 330 degrees
• cos 315 degrees

FAQs on Cos 108 Degrees

What is Cos 108 Degrees?

Cos 108 degrees is the value of cosine trigonometric function for an angle equal to 108 degrees. The value of cos 108° is (1 - √5)/4 or -0.309 (approx)

How to Find the Value of Cos 108 Degrees?

The value of cos 108 degrees can be calculated by constructing an angle of 108° with the x-axis, and then finding the coordinates of the corresponding point (-0.309, 0.9511) on the unit circle. The value of cos 108° is equal to the x-coordinate (-0.309). ∴ cos 108° = -0.309.

What is the Value of Cos 108 Degrees in Terms of Sin 108°?

Using trigonometric identities, we can write cos 108° in terms of sin 108° as, cos(108°) = -√(1 - sin²(108°)). Here, the value of sin 108° is equal to 0.9511.

How to Find Cos 108° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 108° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(108°))
• ± 1/√(1 + tan²(108°))
• ± cot 108°/√(1 + cot²(108°))
• ± √(cosec²(108°) - 1)/cosec 108°
• 1/sec 108°

☛ Also check: trigonometric table

What is the Value of Cos 108° in Terms of Sec 108°?

Since the secant function is the reciprocal of the cosine function, we can write cos 108° as 1/sec(108°). The value of sec 108° is equal to -3.236067.