Cos 55 Degrees

The value of cos 55 degrees is 0.5735764. . .. Cos 55 degrees in radians is written as cos (55° × π/180°), i.e., cos (11π/36) or cos (0.959931. . .). In this article, we will discuss the methods to find the value of cos 55 degrees with examples.

• Cos 55°: 0.5735764. . .
• Cos (-55 degrees): 0.5735764. . .
• Cos 55° in radians: cos (11π/36) or cos (0.9599310 . . .)

What is the Value of Cos 55 Degrees?

The value of cos 55 degrees in decimal is 0.573576436. . .. Cos 55 degrees can also be expressed using the equivalent of the given angle (55 degrees) in radians (0.95993 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 55 degrees = 55° × (π/180°) rad = 11π/36 or 0.9599 . . .
∴ cos 55° = cos(0.9599) = 0.5735764. . .

Explanation:

For cos 55 degrees, the angle 55° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 55° value = 0.5735764. . .
Since the cosine function is a periodic function, we can represent cos 55° as, cos 55 degrees = cos(55° + n × 360°), n ∈ Z.
⇒ cos 55° = cos 415° = cos 775°, and so on.
Note: Since, cosine is an even function, the value of cos(-55°) = cos(55°).

Methods to Find Value of Cos 55 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 55° is given as 0.57357. . .. We can find the value of cos 55 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 55° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 55 degrees as:

• ± √(1-sin²(55°))
• ± 1/√(1 + tan²(55°))
• ± cot 55°/√(1 + cot²(55°))
• ±√(cosec²(55°) - 1)/cosec 55°
• 1/sec 55°

Note: Since 55° lies in the 1st Quadrant, the final value of cos 55° will be positive.

We can use trigonometric identities to represent cos 55° as,

• -cos(180° - 55°) = -cos 125°
• -cos(180° + 55°) = -cos 235°
• sin(90° + 55°) = sin 145°
• sin(90° - 55°) = sin 35°

Cos 55 Degrees Using Unit Circle

To find the value of cos 55 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 55° angle with the positive x-axis.
• The cos of 55 degrees equals the x-coordinate(0.5736) of the point of intersection (0.5736, 0.8192) of unit circle and r.

Hence the value of cos 55° = x = 0.5736 (approx)

☛ Also Check:

• cos 20 degrees
• cos 225 degrees
• cos 21 degrees
• cos 780 degrees
• cos 32 degrees
• cos 260 degrees

FAQs on Cos 55 Degrees

What is Cos 55 Degrees?

Cos 55 degrees is the value of cosine trigonometric function for an angle equal to 55 degrees. The value of cos 55° is 0.5736 (approx)

What is the Value of Cos 55 Degrees in Terms of Cot 55°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 55° can be written as cot 55°/√(1 + cot²(55°)). Here, the value of cot 55° is equal to 0.70020.

How to Find Cos 55° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 55° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(55°))
• ± 1/√(1 + tan²(55°))
• ± cot 55°/√(1 + cot²(55°))
• ± √(cosec²(55°) - 1)/cosec 55°
• 1/sec 55°

☛ Also check: trigonometry table

What is the Value of Cos 55° in Terms of Cosec 55°?

Since the cosine function can be represented using the cosecant function, we can write cos 55° as [√(cosec²(55°) - 1)/cosec 55°]. The value of cosec 55° is equal to 1.22077.

How to Find the Value of Cos 55 Degrees?

The value of cos 55 degrees can be calculated by constructing an angle of 55° with the x-axis, and then finding the coordinates of the corresponding point (0.5736, 0.8192) on the unit circle. The value of cos 55° is equal to the x-coordinate (0.5736). ∴ cos 55° = 0.5736.