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:
 ± √(1sin²(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 xaxis.
 The cos of 53 degrees equals the xcoordinate(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:
Examples Using Cos 53 Degrees

Example 1: Find the value of (cos² 26.5°  sin² 26.5°). [Hint: Use cos 53° = 0.6018]
Solution:
Using the cos 2a formula,
(cos² 26.5°  sin² 26.5°) = cos(2 × 26.5°) = cos 53°
∵ cos 53° = 0.6018
⇒ (cos² 26.5°  sin² 26.5°) = 0.6018 
Example 2: Using the value of cos 53°, solve: (1sin²(53°)).
Solution:
We know, (1sin²(53°)) = (cos²(53°)) = 0.3622
⇒ (1sin²(53°)) = 0.3622 
Example 3: Simplify: 8 (cos 53°/sin 143°)
Solution:
We know cos 53° = sin 143°
⇒ 8 cos 53°/sin 143° = 8 (cos 53°/cos 53°)
= 8(1) = 8
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:
 ± √(1sin²(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 xaxis, 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 xcoordinate (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.
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