Cos 54 Degrees

The value of cos 54 degrees is 0.5877852. . .. Cos 54 degrees in radians is written as cos (54° × π/180°), i.e., cos (3π/10) or cos (0.942477. . .). In this article, we will discuss the methods to find the value of cos 54 degrees with examples.

• Cos 54°: 0.5877852. . .
• Cos 54° in fraction: √(10 - 2√5)/4
• Cos (-54 degrees): 0.5877852. . .
• Cos 54° in radians: cos (3π/10) or cos (0.9424777 . . .)

What is the Value of Cos 54 Degrees?

The value of cos 54 degrees in decimal is 0.587785252. . .. Cos 54 degrees can also be expressed using the equivalent of the given angle (54 degrees) in radians (0.94247 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 54 degrees = 54° × (π/180°) rad = 3π/10 or 0.9424 . . .
∴ cos 54° = cos(0.9424) = √(10 - 2√5)/4 or 0.5877852. . .

Explanation:

For cos 54 degrees, the angle 54° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 54° value = √(10 - 2√5)/4 or 0.5877852. . .
Since the cosine function is a periodic function, we can represent cos 54° as, cos 54 degrees = cos(54° + n × 360°), n ∈ Z.
⇒ cos 54° = cos 414° = cos 774°, and so on.
Note: Since, cosine is an even function, the value of cos(-54°) = cos(54°).

Methods to Find Value of Cos 54 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 54° is given as 0.58778. . .. We can find the value of cos 54 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 54 Degrees Using Unit Circle

To find the value of cos 54 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 54° angle with the positive x-axis.
• The cos of 54 degrees equals the x-coordinate(0.5878) of the point of intersection (0.5878, 0.809) of unit circle and r.

Hence the value of cos 54° = x = 0.5878 (approx)

Cos 54° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 54 degrees as:

• ± √(1-sin²(54°))
• ± 1/√(1 + tan²(54°))
• ± cot 54°/√(1 + cot²(54°))
• ±√(cosec²(54°) - 1)/cosec 54°
• 1/sec 54°

Note: Since 54° lies in the 1st Quadrant, the final value of cos 54° will be positive.

We can use trigonometric identities to represent cos 54° as,

• -cos(180° - 54°) = -cos 126°
• -cos(180° + 54°) = -cos 234°
• sin(90° + 54°) = sin 144°
• sin(90° - 54°) = sin 36°

☛ Also Check:

• cos 270 degrees
• cos 10 degrees
• cos 210 degrees
• cos 95 degrees
• cos 71 degrees
• cos 57 degrees

FAQs on Cos 54 Degrees

What is Cos 54 Degrees?

Cos 54 degrees is the value of cosine trigonometric function for an angle equal to 54 degrees. The value of cos 54° is √(10 - 2√5)/4 or 0.5878 (approx)

What is the Value of Cos 54° in Terms of Cosec 54°?

Since the cosine function can be represented using the cosecant function, we can write cos 54° as [√(cosec²(54°) - 1)/cosec 54°]. The value of cosec 54° is equal to 1.23606.

How to Find Cos 54° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 54° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(54°))
• ± 1/√(1 + tan²(54°))
• ± cot 54°/√(1 + cot²(54°))
• ± √(cosec²(54°) - 1)/cosec 54°
• 1/sec 54°

☛ Also check: trigonometric table

What is the Value of Cos 54 Degrees in Terms of Tan 54°?

We know, using trig identities, we can write cos 54° as 1/√(1 + tan²(54°)). Here, the value of tan 54° is equal to 1.376381.

How to Find the Value of Cos 54 Degrees?

The value of cos 54 degrees can be calculated by constructing an angle of 54° with the x-axis, and then finding the coordinates of the corresponding point (0.5878, 0.809) on the unit circle. The value of cos 54° is equal to the x-coordinate (0.5878). ∴ cos 54° = 0.5878.