Cos 53 Degrees

The value of cos 53 degrees is 0.6018150. . .. Cos 53 degrees in radians is written as cos (53° × π/180°), i.e., cos (0.925024. . .). In this article, we will discuss the methods to find the value of cos 53 degrees with examples.

• Cos 53°: 0.6018150. . .
• Cos (-53 degrees): 0.6018150. . .
• Cos 53° in radians: cos (0.9250245 . . .)

What is the Value of Cos 53 Degrees?

The value of cos 53 degrees in decimal is 0.601815023. . .. Cos 53 degrees can also be expressed using the equivalent of the given angle (53 degrees) in radians (0.92502 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 53 degrees = 53° × (π/180°) rad = 0.9250 . . .
∴ cos 53° = cos(0.9250) = 0.6018150. . .

Explanation:

For cos 53 degrees, the angle 53° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 53° value = 0.6018150. . .
Since the cosine function is a periodic function, we can represent cos 53° as, cos 53 degrees = cos(53° + n × 360°), n ∈ Z.
⇒ cos 53° = cos 413° = cos 773°, and so on.
Note: Since, cosine is an even function, the value of cos(-53°) = cos(53°).

Methods to Find Value of Cos 53 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 53° is given as 0.60181. . .. We can find the value of cos 53 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 53° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 53 degrees as:

• ± √(1-sin²(53°))
• ± 1/√(1 + tan²(53°))
• ± cot 53°/√(1 + cot²(53°))
• ±√(cosec²(53°) - 1)/cosec 53°
• 1/sec 53°

Note: Since 53° lies in the 1st Quadrant, the final value of cos 53° will be positive.

We can use trigonometric identities to represent cos 53° as,

• -cos(180° - 53°) = -cos 127°
• -cos(180° + 53°) = -cos 233°
• sin(90° + 53°) = sin 143°
• sin(90° - 53°) = sin 37°

Cos 53 Degrees Using Unit Circle

To find the value of cos 53 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 53° angle with the positive x-axis.
• The cos of 53 degrees equals the x-coordinate(0.6018) of the point of intersection (0.6018, 0.7986) of unit circle and r.

Hence the value of cos 53° = x = 0.6018 (approx)

☛ Also Check:

• cos 37 degrees
• cos 3 degrees
• cos 225 degrees
• cos 47 degrees
• cos 9 degrees
• cos 244 degrees

FAQs on Cos 53 Degrees

What is Cos 53 Degrees?

Cos 53 degrees is the value of cosine trigonometric function for an angle equal to 53 degrees. The value of cos 53° is 0.6018 (approx)

What is the Value of Cos 53° in Terms of Cosec 53°?

Since the cosine function can be represented using the cosecant function, we can write cos 53° as [√(cosec²(53°) - 1)/cosec 53°]. The value of cosec 53° is equal to 1.25213.

How to Find Cos 53° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 53° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(53°))
• ± 1/√(1 + tan²(53°))
• ± cot 53°/√(1 + cot²(53°))
• ± √(cosec²(53°) - 1)/cosec 53°
• 1/sec 53°

☛ Also check: trigonometry table

How to Find the Value of Cos 53 Degrees?

The value of cos 53 degrees can be calculated by constructing an angle of 53° with the x-axis, and then finding the coordinates of the corresponding point (0.6018, 0.7986) on the unit circle. The value of cos 53° is equal to the x-coordinate (0.6018). ∴ cos 53° = 0.6018.

What is the Value of Cos 53 Degrees in Terms of Tan 53°?

We know, using trig identities, we can write cos 53° as 1/√(1 + tan²(53°)). Here, the value of tan 53° is equal to 1.327044.