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Cos 39 Degrees
The value of cos 39 degrees is 0.7771459. . .. Cos 39 degrees in radians is written as cos (39° × π/180°), i.e., cos (13π/60) or cos (0.680678. . .). In this article, we will discuss the methods to find the value of cos 39 degrees with examples.
 Cos 39°: 0.7771459. . .
 Cos (39 degrees): 0.7771459. . .
 Cos 39° in radians: cos (13π/60) or cos (0.6806784 . . .)
What is the Value of Cos 39 Degrees?
The value of cos 39 degrees in decimal is 0.777145961. . .. Cos 39 degrees can also be expressed using the equivalent of the given angle (39 degrees) in radians (0.68067 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 39 degrees = 39° × (π/180°) rad = 13π/60 or 0.6806 . . .
∴ cos 39° = cos(0.6806) = 0.7771459. . .
Explanation:
For cos 39 degrees, the angle 39° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 39° value = 0.7771459. . .
Since the cosine function is a periodic function, we can represent cos 39° as, cos 39 degrees = cos(39° + n × 360°), n ∈ Z.
⇒ cos 39° = cos 399° = cos 759°, and so on.
Note: Since, cosine is an even function, the value of cos(39°) = cos(39°).
Methods to Find Value of Cos 39 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 39° is given as 0.77714. . .. We can find the value of cos 39 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cos 39° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 39 degrees as:
 ± √(1sin²(39°))
 ± 1/√(1 + tan²(39°))
 ± cot 39°/√(1 + cot²(39°))
 ±√(cosec²(39°)  1)/cosec 39°
 1/sec 39°
Note: Since 39° lies in the 1st Quadrant, the final value of cos 39° will be positive.
We can use trigonometric identities to represent cos 39° as,
 cos(180°  39°) = cos 141°
 cos(180° + 39°) = cos 219°
 sin(90° + 39°) = sin 129°
 sin(90°  39°) = sin 51°
Cos 39 Degrees Using Unit Circle
To find the value of cos 39 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 39° angle with the positive xaxis.
 The cos of 39 degrees equals the xcoordinate(0.7771) of the point of intersection (0.7771, 0.6293) of unit circle and r.
Hence the value of cos 39° = x = 0.7771 (approx)
☛ Also Check:
Examples Using Cos 39 Degrees

Example 1: Find the value of (cos² 19.5°  sin² 19.5°). [Hint: Use cos 39° = 0.7771]
Solution:
Using the cos 2a formula,
(cos² 19.5°  sin² 19.5°) = cos(2 × 19.5°) = cos 39°
∵ cos 39° = 0.7771
⇒ (cos² 19.5°  sin² 19.5°) = 0.7771 
Example 2: Simplify: 9 (cos 39°/sin 129°)
Solution:
We know cos 39° = sin 129°
⇒ 9 cos 39°/sin 129° = 9 (cos 39°/cos 39°)
= 9(1) = 9 
Example 3: Find the value of cos 39° if sec 39° is 1.2867.
Solution:
Since, cos 39° = 1/sec 39°
⇒ cos 39° = 1/1.2867 = 0.7771
FAQs on Cos 39 Degrees
What is Cos 39 Degrees?
Cos 39 degrees is the value of cosine trigonometric function for an angle equal to 39 degrees. The value of cos 39° is 0.7771 (approx)
How to Find Cos 39° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 39° can be given in terms of other trigonometric functions as:
 ± √(1sin²(39°))
 ± 1/√(1 + tan²(39°))
 ± cot 39°/√(1 + cot²(39°))
 ± √(cosec²(39°)  1)/cosec 39°
 1/sec 39°
☛ Also check: trigonometry table
How to Find the Value of Cos 39 Degrees?
The value of cos 39 degrees can be calculated by constructing an angle of 39° with the xaxis, and then finding the coordinates of the corresponding point (0.7771, 0.6293) on the unit circle. The value of cos 39° is equal to the xcoordinate (0.7771). ∴ cos 39° = 0.7771.
What is the Value of Cos 39 Degrees in Terms of Sin 39°?
Using trigonometric identities, we can write cos 39° in terms of sin 39° as, cos(39°) = √(1  sin²(39°)). Here, the value of sin 39° is equal to 0.6293.
What is the Value of Cos 39° in Terms of Cosec 39°?
Since the cosine function can be represented using the cosecant function, we can write cos 39° as [√(cosec²(39°)  1)/cosec 39°]. The value of cosec 39° is equal to 1.58901.
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